Authors:Jinyi Sun; Minghua Yang; Shangbin Cui Pages: 1203 - 1229 Abstract: Abstract We study the three-dimensional Navier–Stokes equations in the rotational framework. By using the Littlewood–Paley analysis technique and the dispersive estimates for the Coriolis linear group \(\{e^{\pm i\Omega t\frac{D_3}{ D }}\}_{t\in \mathbb {R}}\) , we prove unique existence of global mild solutions to initial value problem and mild solutions to time-periodic problem of the rotating Navier–Stokes equations under some precise conditions, respectively, which permit the initial velocity and the time-periodic external force to be arbitrarily large provided that the speed of the rotation is fast enough. These results improve the related ones obtained in Iwabuchi and Takada (Math Ann 357:727–741, 2013) and Koh et al. (Adv diff Equ 19:857–878, 2014), and the result on the time-periodic problem can also be regarded as an enhancement and complement of that in Iwabuchi and Takada (J Evol Equ 12:985–1000, 2012). Meanwhile, based on the so-called Gevrey estimates, which are motivated by the work of Foias and Temam (J Funct Anal 87:359–369, 1989), we particularly verify that the obtained mild solutions are analytic in the spatial variables. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0613-4 Issue No:Vol. 196, No. 4 (2017)

Authors:M. P. Dussan; A. P. Franco Filho; M. Magid Pages: 1231 - 1249 Abstract: Abstract In this paper, we extend and solve the Björling problem for timelike surfaces in the ambient space \({\mathbb {R}}^{4}_{1}\) . To do this, we define a Gauss map ideally suited to this setting using the split-complex variable and then we obtain a Weierstrass representation formula. We use this to construct new examples and give applications. In particular, we obtain one-parameter families of timelike surfaces in \({\mathbb {R}}^{4}_{1}\) which are solutions of the timelike Björling problem. In addition, we establish symmetry principles for the class of minimal timelike surfaces in \({\mathbb {R}}^4_1\) . PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0614-3 Issue No:Vol. 196, No. 4 (2017)

Authors:Enrico Le Donne; Sebastiano Nicolussi-Golo; Andrea Sambusetti Pages: 1251 - 1272 Abstract: Abstract The paper is devoted to the large-scale geometry of the Heisenberg group \({\mathbb {H}}\) equipped with left-invariant Riemannian metrics. We prove that two such metrics have bounded difference if and only if they are asymptotic, i.e., their ratio goes to one at infinity. Moreover, we show that for every left-invariant Riemannian metric d on \({\mathbb {H}}\) there is a unique subRiemannian metric \(d'\) for which \(d-d'\) goes to zero at infinity, and we estimate the rate of convergence. As a first immediate consequence, we get that the Riemannian Heisenberg group is at bounded distance from its asymptotic cone. The second consequence, which was our aim, is the explicit description of the horoboundary of the Riemannian Heisenberg group. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0615-2 Issue No:Vol. 196, No. 4 (2017)

Authors:Simone Borghesi; Giuseppe Tomassini Pages: 1273 - 1306 Abstract: Abstract In this article we give two notions of hyperbolicity for groupoids on the analytic site of complex spaces, which we call Kobayashi and Brody hyperbolicity. In the special case the groupoid is a complex analytic space, these notions of hyperbolicity give the classical ones due to Kobayashi and Brody. We prove that such notions are equivalent if the groupoid is a compact Deligne–Mumford analytic stack (in analogy with the Brody theorem). Moreover, under the same assumptions, such notions of hyperbolicity are completely detected by the coarse moduli space of the stack. We finally show that stack hyperbolicity, as we defined it, is expected to impose a peculiar behavior to the stack itself, much like hyperbolicity for complex spaces. For instance, a stronger notion of it (hyperbolicity of the coarse moduli space) implies a “strong asymmetry” on the stack in the compact case, namely that its automorphism 2-group has only finitely many isomorphism classes. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0616-1 Issue No:Vol. 196, No. 4 (2017)

Authors:Young Jin Suh; Doo Hyun Hwang Pages: 1307 - 1326 Abstract: Abstract First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric \({Q^m}^* = SO^{o}_{m,2}/SO_mSO_2\) . Next, we give a complete proof of non-existence of real hypersurfaces in \({Q^m}^* = SO^{o}_{m,2}/SO_mSO_2\) with shape operator of Codazzi type. Motivated by this result, we give a complete classification of real hypersurfaces in \({Q^m}^* = SO^{o}_{m,2}/SO_mSO_2\) with Reeb parallel shape operator. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0617-0 Issue No:Vol. 196, No. 4 (2017)

Authors:Serena Dipierro; Hans-Christoph Grunau Pages: 1327 - 1344 Abstract: Abstract Boggio’s formula in balls is known for integer-polyharmonic Dirichlet problems and for fractional Dirichlet problems with fractional parameter less than 1. We give here a consistent formulation for fractional polyharmonic Dirichlet problems such that Boggio’s formula in balls yields solutions also for the general fractional case. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0618-z Issue No:Vol. 196, No. 4 (2017)

Authors:Ana M. Lerma; José M. Manzano Pages: 1345 - 1364 Abstract: Abstract A Killing submersion is a Riemannian submersion from a 3-manifold to a surface, both connected and orientable, whose fibers are the integral curves of a Killing vector field, not necessarily unitary. The first part of this paper deals with the classification of all Killing submersions in terms of two geometric functions, namely the bundle curvature and the length of the Killing vector field, which can be prescribed arbitrarily. In a second part, we show that if the base is compact and the submersion admits a global section, then it also admits a global minimal section. These turn out to be the only global sections with constant mean curvature, which solves the Bernstein problem in Killing submersions over compact base surfaces, as well as the Plateau problem with empty boundary. Finally, we prove that any compact orientable stable surface with constant mean curvature immersed in the total space of a Killing submersion must be either an entire minimal section or everywhere tangent to the Killing direction. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0619-y Issue No:Vol. 196, No. 4 (2017)

Authors:Pricila S. Barbosa; Antônio L. Pereira; Marcone C. Pereira Pages: 1365 - 1398 Abstract: Abstract We consider here the family of semilinear parabolic problems $$\begin{aligned} \begin{array}{lll} \left\{ \begin{array}{lll} u_t(x,t)&{}=&{}\Delta u(x,t) -au(x,t) + f(u(x,t)) ,\quad x \in \Omega _\epsilon \quad {\text {and}}\quad t>0,\\ \displaystyle \frac{\partial u}{\partial N}(x,t)&{}=&{}g(u(x,t)), \quad x \in \partial \Omega _\epsilon \quad {\text {and}}\quad t>0, \end{array} \right. \end{array} \end{aligned}$$ where \(\Omega \) is the unit square, \(\Omega _{\epsilon }=h_{\epsilon }(\Omega )\) , and \(h_{\epsilon }\) is a family of diffeomorphisms converging to the identity in the \(C^1\) -norm. We show that the problem is well posed for \(\epsilon >0\) sufficiently small in a suitable phase space, the associated semigroup has a global attractor \({\mathcal {A}}_{\epsilon }\) , and the family \(\{{\mathcal {A}}_{\epsilon }\}_{\epsilon \ge 0}\) is continuous at \(\epsilon = 0\) . PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0620-5 Issue No:Vol. 196, No. 4 (2017)

Authors:Liliane A. Maia; Benedetta Pellacci Pages: 1399 - 1430 Abstract: Abstract The existence of a positive solution for a class of asymptotically linear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter function. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0621-4 Issue No:Vol. 196, No. 4 (2017)

Authors:Giuseppina Barletta; Pasquale Candito; Salvatore A. Marano; Kanishka Perera Pages: 1431 - 1440 Abstract: Abstract We prove the existence of N distinct pairs of nontrivial solutions for critical p-Laplacian problems in \(\mathbb R^N\) , as well as in bounded domains. To overcome the difficulties arising from the lack of compactness, we use a recent global compactness result of Mercuri and Willem. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0622-3 Issue No:Vol. 196, No. 4 (2017)

Authors:Guglielmo Feltrin Pages: 1441 - 1458 Abstract: Abstract We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel’skiĭ ones. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0623-2 Issue No:Vol. 196, No. 4 (2017)

Authors:Ming Xu; Shaoqiang Deng Pages: 1459 - 1488 Abstract: Abstract In this paper, we use the flag curvature formula for homogeneous Finsler spaces in our previous work to classify odd-dimensional smooth coset spaces admitting positively curved reversible homogeneous Finsler metrics. We will show that most important features of L. Bérard-Bergery’s classification results for odd-dimensional positively curved Riemannian homogeneous spaces can be generalized to reversible Finsler spaces. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0624-1 Issue No:Vol. 196, No. 4 (2017)

Authors:Nguyen Thac Dung; Keomkyo Seo Pages: 1489 - 1511 Abstract: Abstract In this paper, we study the connectedness at infinity of complete submanifolds by using the theory of p-harmonic function. For lower-dimensional cases, we prove that if M is a complete orientable noncompact hypersurface in \(\mathbb {R}^{n+1}\) and if \(\delta \) -stability inequality holds on M, then M has only one p-nonparabolic end. It is also proved that if \(M^n\) is a complete noncompact submanifold in \({\mathbb {R}}^{n+k}\) with sufficiently small \(L^n\) norm of the traceless second fundamental form, then M has only one p-nonparabolic end. Moreover, we obtain a lower bound of the fundamental tone of the p Laplace operator on complete submanifolds in a Riemannian manifold. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0625-0 Issue No:Vol. 196, No. 4 (2017)

Authors:Rafael López Pages: 1513 - 1524 Abstract: Abstract Given two circles contained in parallel planes, it is expectable that there does not exist a doubly connected minimal surface bounded by both circles if these circles are either laterally or vertically far away. In this paper, we give a quantitative estimate of this separation. We also obtain bounds for the height of a Riemann minimal example in terms of a catenoid with the same boundary radii and waist. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0626-z Issue No:Vol. 196, No. 4 (2017)

Authors:Eloisa Detomi; Marta Morigi; Pavel Shumyatsky Pages: 1525 - 1535 Abstract: Abstract Let \(\mathcal {N}\) be the class of pronilpotent groups, or the class of locally nilpotent profinite groups, or the class of strongly locally nilpotent profinite groups. It is proved that a profinite group G is finite-by- \(\mathcal {N}\) if and only if G is covered by countably many \(\mathcal {N}\) -subgroups. The commutator subgroup \(G'\) is finite-by- \(\mathcal {N}\) if and only if the set of all commutators in G is covered by countably many \(\mathcal {N}\) -subgroups. Here, a group is strongly locally nilpotent if it generates a locally nilpotent variety of groups. According to Zelmanov, a locally nilpotent group is strongly locally nilpotent if and only if it is n-Engel for some positive n. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0627-y Issue No:Vol. 196, No. 4 (2017)

Authors:Philippe Laurençot; Christoph Walker Pages: 1537 - 1556 Abstract: Abstract So far most studies on mathematical models for microelectromechanical systems are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the aspect ratio equal to zero in a more complex model involving a moving boundary. A rigorous justification of this derivation is provided here when bending is taken into account. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0628-x Issue No:Vol. 196, No. 4 (2017)

Authors:Elisabetta Chiodaroli; Eduard Feireisl; Ondřej Kreml; Emil Wiedemann Pages: 1557 - 1572 Abstract: Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions' We prove that the answer is negative: generalizing a well-known rigidity result of Ball and James to a more general situation, we construct an explicit measure-valued solution for the compressible Euler equations which cannot be generated by a sequence of distributional solutions. We also give an abstract necessary condition for measure-valued solutions to be generated by weak solutions, relying on work of Fonseca and Müller. While a priori it is not unexpected that not every measure-valued solution arises from a sequence of weak solutions, it is noteworthy that this observation in the compressible case is in contrast to the incompressible situation, where every measure-valued solution can be approximated by weak solutions, as shown by Székelyhidi and Wiedemann. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0629-9 Issue No:Vol. 196, No. 4 (2017)

Authors:Marcos Jardim; Dimitri Markushevich; Alexander S. Tikhomirov Pages: 1573 - 1608 Abstract: Abstract We describe new components of the Gieseker–Maruyama moduli scheme \({\mathcal {M}}(n)\) of semistable rank 2 sheaves E on \({\mathbb {P}^{3}}\) with \(c_1(E)=0\) , \(c_2(E)=n\) and \(c_3(E)=0\) whose generic point corresponds to nonlocally free sheaves. We show that such components grow in number as n grows, and discuss how they intersect the instanton component. As an application, we prove that \({\mathcal {M}}(2)\) is connected, and identify a connected subscheme of \({\mathcal {M}}(3)\) consisting of seven irreducible components. PubDate: 2017-08-01 DOI: 10.1007/s10231-016-0630-3 Issue No:Vol. 196, No. 4 (2017)

Authors:Roman Šimon Hilscher; Petr Zemánek Abstract: 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: 2017-07-26 DOI: 10.1007/s10231-017-0679-7

Authors:E. Rosado María; J. Muñoz Masqué Abstract: Abstract Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, (1) for each second-order Lagrangian density on an arbitrary fibred manifold \(p:E\rightarrow N\) the Poincaré–Cartan form of which is projectable onto \(J^1E\) , by using a new notion of regularity previously introduced, a first-order Hamiltonian formalism is developed for such a class of variational problems; (2) the existence of first-order equivalent Lagrangians is discussed from a local point of view as well as global; (3) this formalism is then applied to classical Hilbert–Einstein Lagrangian and a generalization of the BF theory. The results suggest that the class of problems studied is a natural variational setting for GR. PubDate: 2017-07-18 DOI: 10.1007/s10231-017-0683-y