Related papers: Collared and non-collared manifold boundaries

We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…

We describe an example of an indefinite invariant Einstein metric on a solvmanifold which is not standard, and whose restriction on the nilradical is nondegenerate.

We present some results in the analysis of non-compact differential equations on unbounded domains.

Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…

The goal of this article is to study compact quasi-Einstein manifolds with boundary. We provide boundary estimates for compact quasi-Einstein manifolds simi\-lar to previous results obtained for static and $V$-static spaces. In addition, we…

In this report we consider the parameterization of low-dimensional manifolds that are specified (approximately) by a set of points very close to the manifold in the original high-dimensional space. Our objective is to obtain a…

Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…

We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.

We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold with boundary, and establish a necessary and sufficient…

This is a survey written for a special edition of the journal of differential geometry.

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional…

Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition…

This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics…

Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…

Motivated by a recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with the real line admits a complete metric of bounded negative sectional curvature…

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for compact quasi-Einstein manifolds with boundary that improve some previous results. Moreover, we obtain a…