Related papers: Medial Axis in Pseudo-Euclidean Spaces
Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperk\"ahlerian manifolds as stated by Verbitsky. The initial purpose of this document (which was prepared for a seminar talk) was to extract the…
The aim of this work is to introduce and study some new types of generalizations of pairwise paralindeloff spaces, pairwise nearly paralindeloff and almost paralindeloff spaces. Some of their characterizations, properties and subsets are…
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and…
This paper establishes the conditions under which minimal and stable minimal hypersurfaces are characterized as hyperplanes in Euclidean spaces and as totally geodesic submanifolds in Riemannian manifolds.
We derive some estimates for stable minimal hypersurfaces in $R^{n+1}$. The estimates are related to recent proofs of Bernstein theorems for complete stable minimal hypersurfaces in $R^{n+1}$ for $3\le n\le 5$ by Chodosh-Li,…
This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…
For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.
In this paper, we study a deformation theory of rigid analytic spaces. We develop a theory of cotangent complexes for rigid geometry which fits in with our deformations. We then use the complexes to give a cohomological description of…
We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the…
A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as…
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…
We consider certain point patterns of an Euclidean space and calculate the Ellis enveloping semigroup of their associated dynamical systems. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the…
The paper introduces a number of new techniques to handle minimal hyersurface singularities. In particular, they allow to extend the obstruction theory for postive scalr curvature to any dimension.
Recently geometric hypergraphs that can be defined by intersections of pseudohalfplanes with a finite point set were defined in a purely combinatorial way. This led to extensions of earlier results about points and halfplanes to…
We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…