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 Subjects -> MATHEMATICS (Total: 955 journals)     - APPLIED MATHEMATICS (82 journals)    - GEOMETRY AND TOPOLOGY (20 journals)    - MATHEMATICS (706 journals)    - MATHEMATICS (GENERAL) (43 journals)    - NUMERICAL ANALYSIS (22 journals)    - PROBABILITIES AND MATH STATISTICS (82 journals) MATHEMATICS (706 journals)                  1 2 3 4 | Last

1 2 3 4 | Last

 Annali di Matematica Pura ed Applicata   [SJR: 1.167]   [H-I: 26]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1618-1891 - ISSN (Online) 0373-3114    Published by Springer-Verlag  [2351 journals]
• Hypersurfaces of two space forms and conformally flat hypersurfaces
• Authors: S. Canevari; R. Tojeiro
Pages: 1 - 20
Abstract: We address the problem of determining the hypersurfaces $$f:M^{n} \rightarrow \mathbb {Q}_s^{n+1}(c)$$ with dimension $$n\ge 3$$ of a pseudo-Riemannian space form of dimension $$n+1$$ , constant curvature c and index $$s\in \{0, 1\}$$ for which there exists another isometric immersion $$\tilde{f}:M^{n} \rightarrow \mathbb {Q}^{n+1}_{\tilde{s}}(\tilde{c})$$ with $$\tilde{c}\ne c$$ . For $$n\ge 4$$ , we provide a complete solution by extending results for $$s=0=\tilde{s}$$ by do Carmo and Dajczer (Proc Am Math Soc 86:115–119, 1982) and by Dajczer and Tojeiro (J Differ Geom 36:1–18, 1992). Our main results are for the most interesting case $$n=3$$ , and these are new even in the Riemannian case $$s=0=\tilde{s}$$ . In particular, we characterize the solutions that have dimension $$n=3$$ and three distinct principal curvatures. We show that these are closely related to conformally flat hypersurfaces of $$\mathbb {Q}_s^{4}(c)$$ with three distinct principal curvatures, and we obtain a similar characterization of the latter that improves a theorem by Hertrich-Jeromin (Beitr Algebra Geom 35:315–331, 1994).
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0665-0
Issue No: Vol. 197, No. 1 (2018)

• Enneper representation of minimal surfaces in the three-dimensional
Lorentz–Minkowski space
• Authors: Adriana A. Cintra; Irene I. Onnis
Pages: 21 - 39
Abstract: In this paper, we will give an Enneper-type representation for spacelike and timelike minimal surfaces in the Lorentz–Minkowski space $${\mathbb {L}}^{3}$$ , using the complex and the paracomplex analysis (respectively). Then, we exhibit various examples of minimal surfaces in $${\mathbb {L}}^{3}$$ constructed via the Enneper representation formula that it is equivalent to the Weierstrass representation obtained by Kobayashi (for spacelike immersions) and by Konderak (for the timelike ones).
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0666-z
Issue No: Vol. 197, No. 1 (2018)

• Removable sets for continuous solutions of quasilinear elliptic equations
with nonlinear source or absorption terms
• Authors: Kentaro Hirata; Takayori Ono
Pages: 41 - 59
Abstract: This paper establishes removable singularity theorems for nonnegative continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms when an exceptional set is conditioned in terms of the regularity of Hausdorff measure and a uniform Minkowski property. These weaker conditions enable us to consider some fractal sets as an exceptional set.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0667-y
Issue No: Vol. 197, No. 1 (2018)

• On certain non-hypoelliptic vector fields with finite-codimensional range
on the three-torus
• Authors: Rafael B. Gonzalez
Pages: 61 - 77
Abstract: We study the finiteness of range’s codimension for a class of non-globally hypoelliptic vector fields on a torus of dimension three. The linear dependence of certain interactions of the coefficients is crucial. This condition is close to condition (P) of Nirenberg and Treves. Certain obstructions of number-theoretical nature involving Liouville numbers also appear in the results.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0668-x
Issue No: Vol. 197, No. 1 (2018)

• Estimates of the Green function and the initial-Dirichlet problem for the
heat equation in sub-Riemannian spaces
• Authors: Nicola Garofalo; Isidro H. Munive
Pages: 79 - 108
Abstract: In a cylinder $$D_T = \Omega \times (0,T)$$ , where $$\Omega \subset \mathbb {R}^{n}$$ , we examine the relation between the L-caloric measure, $$\mathrm{d}\omega ^{(x,t)}$$ , where L is the heat operator associated with a system of vector fields of Hörmander type, and the measure $$\mathrm{d}\sigma _X\times \mathrm{d}t$$ , where $$\mathrm{d}\sigma _X$$ is the intrinsic X-perimeter measure. The latter constitutes the appropriate replacement for the standard surface measure on the boundary and plays a central role in sub-Riemannian geometric measure theory. Under suitable assumptions on the domain $$\Omega$$ we establish the mutual absolute continuity of $$\mathrm{d}\omega ^{(x,t)}$$ and $$\mathrm{d}\sigma _X\times \mathrm{d}t$$ . We also derive the solvability of the initial-Dirichlet problem for L with boundary data in appropriate $$L^p$$ spaces, for every $$p>1$$ .
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0669-9
Issue No: Vol. 197, No. 1 (2018)

• Lattice-based integration algorithms: Kronecker sequences and rank-1
lattices
• Authors: Josef Dick; Friedrich Pillichshammer; Kosuke Suzuki; Mario Ullrich; Takehito Yoshiki
Pages: 109 - 126
Abstract: We prove upper bounds on the order of convergence of lattice-based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study worst-case integration errors for Besov spaces of dominating mixed smoothness $$\mathring{\mathbf {B}}^s_{p,\theta }$$ , which also comprise the concept of Sobolev spaces of dominating mixed smoothness $$\mathring{\mathbf {H}}^s_{p}$$ as special cases. The considered algorithms are quasi-Monte Carlo rules with underlying nodes from $$T_N\left( \mathbb {Z}^d\right) \cap [0,1)^d$$ , where $$T_N$$ is a real invertible generator matrix of size d. For such rules, the worst-case error can be bounded in terms of the Zaremba index of the lattice $$\mathbb {X}_N=T_N\left( \mathbb {Z}^d\right)$$ . We apply this result to Kronecker lattices and to rank-1 lattice point sets, which both lead to optimal error bounds up to $$\log N$$ -factors for arbitrary smoothness s. The advantage of Kronecker lattices and classical lattice point sets is that the run-time of algorithms generating these point sets is very short.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0670-3
Issue No: Vol. 197, No. 1 (2018)

• On nearly Sasakian and nearly cosymplectic manifolds
• Authors: Antonio De Nicola; Giulia Dileo; Ivan Yudin
Pages: 127 - 138
Abstract: We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0671-2
Issue No: Vol. 197, No. 1 (2018)

• Complex symplectic structures and the $$\partial {\bar{\partial }}$$ ∂
∂ ¯ -lemma
• Authors: Andrea Cattaneo; Adriano Tomassini
Pages: 139 - 151
Abstract: In this paper, we study complex symplectic manifolds, i.e., compact complex manifolds X which admit a holomorphic (2, 0)-form $$\sigma$$ which is d-closed and non-degenerate, and in particular the Beauville–Bogomolov–Fujiki quadric $$Q_\sigma$$ associated with them. We will show that if X satisfies the $$\partial {\bar{\partial }}$$ -lemma, then $$Q_\sigma$$ is smooth if and only if $$h^{2, 0}(X) = 1$$ and is irreducible if and only if $$h^{1, 1}(X) > 0$$ .
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0672-1
Issue No: Vol. 197, No. 1 (2018)

• Homogenization of an evolution problem with $$L\log L$$ L log L data in a
domain with oscillating boundary
• Authors: Antonio Gaudiello; Olivier Guibé
Pages: 153 - 169
Abstract: We consider a N-dimensional structure, $$N\in \mathbb {N}\setminus \{1\}$$ , with a very rough boundary. Precisely, in 3D the structure consists in a box with the upper side covered with $$\varepsilon$$ -periodically distributed asperities having fixed height and size depending on $$\varepsilon$$ . In this structure, we study the asymptotic behavior, as $$\varepsilon$$ vanishes, of an evolution Neumann problem with source term and initial data having $$L\log L$$ a priori estimates. We identify the limit problem.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0673-0
Issue No: Vol. 197, No. 1 (2018)

• Relations among Gauge and Pettis integrals for cwk ( X )-valued
multifunctions
• Authors: D. Candeloro; L. Di Piazza; K. Musiał; A. R. Sambucini
Pages: 171 - 183
Abstract: The aim of this paper is to study relationships among “gauge integrals” (Henstock, McShane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose, we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems (Theorems 3.2, 4.2, 5.3). As applications of such decompositions, we deduce characterizations of Henstock (Theorem 3.3) and $$\mathcal H$$ (Theorem 4.3) integrable multifunctions, together with an extension of a well-known theorem of Fremlin [22, Theorem 8].
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0674-z
Issue No: Vol. 197, No. 1 (2018)

• Harmonicity of the Atiyah–Hitchin–Singer and Eells–Salamon almost
complex structures
• Authors: Johann Davidov; Oleg Mushkarov
Pages: 185 - 209
Abstract: In this paper, we describe the oriented Riemannian four-manifolds M for which the Atiyah–Hitchin–Singer or Eells–Salamon almost complex structure on the twistor space $${\mathcal {Z}}$$ of M determines a harmonic map from $${\mathcal {Z}}$$ into its twistor space.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0675-y
Issue No: Vol. 197, No. 1 (2018)

• Inequalities for eigenvalues of the buckling problem of arbitrary order
• Authors: Qing-Ming Cheng; Xuerong Qi; Qiaoling Wang; Changyu Xia
Pages: 211 - 232
Abstract: This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the kth eigenvalue in terms of the lower ones independent of the domains. Our results strengthen the recent work in Jost et al. (Commun Partial Differ Equ 35:1563–1589, 2010) and generalize Cheng–Yang’s recent estimates (Cheng and Yang in Trans Am Math Soc 364:6139–6158, 2012) on the buckling eigenvalues of order two to arbitrary order.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0676-x
Issue No: Vol. 197, No. 1 (2018)

• On derivations of subalgebras of real semisimple Lie algebras
• Authors: Paolo Ciatti; Michael G. Cowling
Pages: 233 - 259
Abstract: Let $$\mathfrak {g}$$ be a real semisimple Lie algebra with Iwasawa decomposition $$\mathfrak {k} \oplus \mathfrak {a} \oplus \mathfrak {n}$$ . We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra $$\mathfrak {n}$$ that preserves its restricted root space decomposition is of the form $${\text {ad}}( W)$$ , where $$W \in \mathfrak {m}\oplus \mathfrak {a}$$ .
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0677-9
Issue No: Vol. 197, No. 1 (2018)

• Explicit estimates on the measure of primary KAM tori
• Authors: L. Biasco; L. Chierchia
Pages: 261 - 281
Abstract: From KAM theory it follows that the measure of phase points which do not lie on Diophantine, Lagrangian, “primary” tori in a nearly integrable, real-analytic Hamiltonian system is $$O(\sqrt{\varepsilon })$$ , if $$\varepsilon$$ is the size of the perturbation. In this paper we discuss how the constant in front of $$\sqrt{\varepsilon }$$ depends on the unperturbed system and in particular on the phase-space domain.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0678-8
Issue No: Vol. 197, No. 1 (2018)

• On square integrable solutions and principal and antiprincipal solutions
for linear Hamiltonian systems
• Authors: Roman Šimon Hilscher; Petr Zemánek
Pages: 283 - 306
Abstract: New results in the Weyl–Titchmarsh theory for linear Hamiltonian differential systems are derived by using principal and antiprincipal solutions at infinity. In particular, a non-limit circle case criterion is established and a close connection between the Weyl solution and the minimal principal solution at infinity is shown in the limit point case. In addition, the square integrability of the columns of the minimal principal solution at infinity is investigated. All results are obtained without any controllability assumption. Several illustrative examples are also provided.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0679-7
Issue No: Vol. 197, No. 1 (2018)

• On groups with automorphisms whose fixed points are Engel
• Authors: Cristina Acciarri; Pavel Shumyatsky; Danilo Sanção da Silveira
Pages: 307 - 316
Abstract: We study finite and profinite groups admitting an action by an elementary abelian group under which the centralizers of automorphisms consist of Engel elements. In particular, we prove the following theorems. Let q be a prime and A an elementary abelian q-group of order $$q^2$$ acting coprimely on a profinite group G. Assume that all elements in $$C_{G}(a)$$ are Engel in G for each $$a\in A^{\#}$$ . Then, G is locally nilpotent. Let q be a prime, n a positive integer and A an elementary abelian group of order $$q^3$$ acting coprimely on a finite group G. Assume that for each $$a\in A^{\#}$$ every element of $$C_{G}(a)$$ is n-Engel in $$C_{G}(a)$$ . Then, the group G is k-Engel for some $$\{n,q\}$$ -bounded number k.
PubDate: 2018-02-01
DOI: 10.1007/s10231-017-0680-1
Issue No: Vol. 197, No. 1 (2018)

• Permutability in uncountable groups
• Authors: M. De Falco; M. J. Evans; F. de Giovanni; C. Musella
Abstract: A subgroup X of a group G is called permutable if $$XY=YX$$ for all subgroups Y of G. It is well known that permutable subgroups play an important role in many problems in group theory, and the purpose of this paper is to describe the structure of uncountable groups of regular cardinality  $$\aleph$$ in which all large subgroups are permutable.
PubDate: 2018-02-21
DOI: 10.1007/s10231-018-0730-3

• Parabolic BMO and the forward-in-time maximal operator
• Authors: Olli Saari
Abstract: We study if the parabolic forward-in-time maximal operator is bounded on parabolic $${{\mathrm{BMO}}}$$ . It turns out that for non-negative functions the answer is positive, but the behavior of sign-changing functions is more delicate. The class parabolic $${{\mathrm{BMO}}}$$ and the forward-in-time maximal operator originate from the regularity theory of nonlinear parabolic partial differential equations. In addition to that context, we also study the question in dimension one.
PubDate: 2018-02-20
DOI: 10.1007/s10231-018-0733-0

• Infinitely many sign-changing solutions for a nonlocal problem
• Authors: Guangze Gu; Wei Zhang; Fukun Zhao
Abstract: In this paper, we consider the following general nonlocal problem \begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\mathcal {L}_K u=f(x,u)&{}\text {in} \,\,\varOmega ,\\ u=0&{}\text {in}\,\,\mathbb {R}^N\backslash \varOmega , \end{array} \right. \end{aligned} where $$\varOmega \subset \mathbb {R}^N$$ is a bounded domain with Lipschitz boundary $$\partial \varOmega$$ , $$s\in (0,1)$$ with $$2s<N$$ and $$\mathcal {L}_K$$ is a nonlocal integrodifferential operator of fractional Laplacian type. We obtain the existence of infinitely many sign-changing solutions by combining critical point theory and invariant sets of descending flow.
PubDate: 2018-02-17
DOI: 10.1007/s10231-018-0731-2

• Kinematic formulae for tensorial curvature measures
• Authors: Daniel Hug; Jan A. Weis
Abstract: The tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. On convex polytopes, there exist further generalizations some of which also have continuous extensions to arbitrary convex bodies. We prove a complete set of kinematic formulae for such (generalized) tensorial curvature measures. These formulae express the integral mean of the (generalized) tensorial curvature measure of the intersection of two given convex bodies (resp. polytopes), one of which is uniformly moved by a proper rigid motion, in terms of linear combinations of (generalized) tensorial curvature measures of the given convex bodies (resp. polytopes). We prove these results in a more direct way than in the classical proof of the principal kinematic formula for curvature measures, which uses the connection to Crofton formulae to determine the involved constants explicitly.
PubDate: 2018-01-30
DOI: 10.1007/s10231-018-0728-x

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