We prove Reilly-type upper bounds for divergence-type operators of the second order as well Steklov problems on submanifolds Riemannian manifolds bounded sectional curvature endowed with a weighted measure.

In the framework of digital topology, we study structural and topological properties of digital ndimensional manifolds. We introduce the notion of simple connectedness of a digital space and prove that if M and N are homotopy equivalent digital spaces and M is simply connected, then so is N. We show that a simply connected digital 2-manifold is the digital 2-sphere and a simply connected digita...

There are several algebraic analogues of the JSJ–decomposition of a 3–manifold, one of which was described by the authors. We study this analogue in the special case of Poincaré duality pairs. Introduction In [23], we obtained canonical decompositions for almost finitely presented groups analogous to the JSJ–decomposition of a 3–manifold. In particular, for many almost finitely presented groups...

In this note, we propose Steklov-Poincaré iterative algorithms (mutu-ated from the analogy with heterogeneous domain decomposition) to solve fluid-structure interaction problems. Although our framework is very general, the driving application is concerned with the interaction of blood flow and vessel wall in large arteries.

Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced.

We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and subsurface flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov-Poincaré operators, and we prove its wellposedness.

A. Mari, ∗ V. Giovannetti, A. S. Holevo, 3 R. Garćıa-Patrón, 5 and N. J. Cerf NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy. Steklov Mathematical Institute, 119991 Moscow, Russia National Research University Higher School of Economics (HSE) 4 QuIC, Ecole Polytechnique de Bruxelles, 1050 Bruxelles, Belgium Max-Planck-Institut für Quantenoptik, D-85748 Garching,...

In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components are eigenfunctions Jacobi-Steklov operator, then surface must be rotationally symmetric.

A. Vagov, 2 H. Schomerus, and V. V. Zalipaev 4 Institut für Theoretische Physik III, Bayreuth Universität, Bayreuth 95440, Germany Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Steklov Mathematical Institute, Fontanka 27, St.-Petersburg 191023, Russia 4 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom (Dated: July 9...

In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion H(Ω) ↪→ L(∂Ω) for functions that vanish in a subset of Ω. This problem is also related to a minimization problem for Steklov eigenvalues.