Related papers: Integral geometry and Mizel's problem
We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We study some Diophantine problems related to triangles with two given integral sides. We solve two problems posed by Zolt\'an Bertalan and we also provide some generalization.
In this article, we shall discuss the solution to the Zariski Cancellation Problem in positive characteristic, various approaches taken so far towards the possible solution in characteristic zero, and several other questions related to this…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this geometric construction is described leading to…
We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
We discuss solutions of several questions concerning the geometry of conformal planes.
In this paper we study the dual Orlicz-Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
We resolve a long-standing open problem posed by Federer concerning the rectifiability of the integral geometric measure with exponent p >1, thereby settling a question that has persisted since its formulation. While the main theorem is…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.