Related papers: A note on subsets of positive reach
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide…
We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular,…
Defining the $m$-th stratum of a closed subset of an $n$ dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least $n-m$ linearly independent directions, we establish that the $m$-th stratum is…
We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…
The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the…
Riemannian metrics of positive Ricci curvature were constructed on certain moment-angle manifolds.
We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
In this paper we use a dynamical approach to prove some new divergence theorems on complete non-compact Riemannian manifolds.
We present a new construction for obtaining pairs of higher-step isospectral Riemannian nilmanifolds and compare several resulting new examples. In particular, we present new examples of manifolds that are isospectral on functions, but not…
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class $C^{1,1}$. These results are then used to prove new alternating Steiner formul{\ae} for…
This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal…
Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension are studied. Such structures are constructed on hyperspheres in 4-dimensional spaces, Euclidean and pseudo-Euclidean, respectively. The obtained manifolds…
The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete…
We give asymptotically tight estimates of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifolds. We show that the result follows directly from structural properties…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
Some geometric structures with associated Riemannian metrics have been considered in the book.