Related papers: Medial Axis in Pseudo-Euclidean Spaces
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…
We discuss pseudoduality transformations in two dimensional conformally invariant classical sigma models, and extend our analysis to a given boundaries of world-sheet, which gives rise to an appropriate framework for the discussion of the…
We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable…
Many classical facts in Riemannian geometry have their pseudo-Riemannian analogs. For instance, the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian…
The main objective of this paper is to survey some recent results on the Chern--Moser question concerning existence of umbilical points on three dimensional CR submanifolds in $\mathbb C^2$.
A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chv\'tal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was…
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.
There are many problems and configurations in Euclidean geometry that were never extended to the framework of (normed or) finite dimensional real Banach spaces, although their original versions are inspiring for this type of generalization,…
We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.
This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after…
A pseudoclassical model is proposed to describe massive Dirac (spin one-half) particles in arbitrary odd dimensions. The quantization of the model reproduces the minimal quantum theory of spinning particles in such dimensions. A dimensional…
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…
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…
Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counterpart to convex bodies containing the origin in the…
We study no-boundary de Sitter extremal surfaces and their pseudo-entropy areas for generic subregions at the future boundary, building on previous work. For large subregions, timelike+Euclidean extremal surfaces exist with transparent…
Suppose that a metric space $X$ is the union of two metric subspaces $A$ and $B$ that embed into Euclidean space with distortions $D_A$ and $D_B$, respectively. We prove that then $X$ embeds into Euclidean space with a bounded distortion…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…
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