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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

Authors:A. Altavilla; C. de Fabritiis Abstract: We study global properties of quaternionic slice regular functions (also called s-regular) defined on symmetric slice domains. In particular, thanks to new techniques and points of view, we can characterize the property of being one-slice preserving in terms of the projectivization of the vectorial part of the function. We also define a “Hermitian” product on slice regular functions which gives us the possibility to express the \(*\) -product of two s-regular functions in terms of the scalar product of suitable functions constructed starting from f and g. Afterwards we are able to determine, under different assumptions, when the sum, the \(*\) -product and the \(*\) -conjugation of two slice regular functions preserve a complex slice. We also study when the \(*\) -power of a slice regular function has this property or when it preserves all complex slices. To obtain these results, we prove two factorization theorems: in the first one, we are able to split a slice regular function into the product of two functions: one keeping track of the zeroes and the other which is never vanishing; in the other one, we give necessary and sufficient conditions for a slice regular function (which preserves all complex slices) to be the symmetrized of a suitable slice regular one. PubDate: 2018-01-29 DOI: 10.1007/s10231-018-0724-1

Authors:Vincenzo Recupero; Filippo Santambrogio Abstract: We present a generalized formulation of sweeping process where the behavior of the solution is prescribed at the jump points of the driving moving set. An existence and uniqueness theorem for such formulation is proved. As a consequence we derive a formulation and an existence/uniqueness theorem for sweeping processes driven by an arbitrary \({\textit{BV}}\) moving set, whose evolution is not necessarily right continuous. Applications to the play operator of elastoplasticity are also shown. PubDate: 2018-01-27 DOI: 10.1007/s10231-018-0726-z

Authors:Xiaopeng Zhao Abstract: In this paper, we consider the global well-posedness of solutions for the Cauchy problem of N-dimensional Cahn–Hilliard equation with convective term. We first construct the local smooth solutions; then, by combining some a priori estimates, continuity argument, the local smooth solutions are extended step by step to all \(t>0\) provided that the initial data are suitably small and the smooth nonlinear functions satisfy certain local growth conditions at some fixed point \({\bar{u}}\in {\mathbb {R}}\) . In addition, for the N-dimensional Cahn–Hilliard equation without convective term, we also establish the similar result. PubDate: 2018-01-25 DOI: 10.1007/s10231-018-0727-y