Related papers: On the planar Lp-Minkowski problem

This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric…

In this paper, we consider the $L_p$ dual Minkowski problem for capillary hypersurfaces for $p>q$ and $q\leq 1$, which aims to find a capillary convex body with a prescribed capillary $(p,q)$-th dual curvature measure in the Euclidean…

We study the problem of correct solvability in the space $L_p(\mathbb R),$ $p\in[1,\infty)$ of the equation $$ -(r(x) y'(x))'+q(x)y(x)=f(x),\quad x\in \mathbb R $$ under the conditions $$r>0,\quad q\ge 0,\quad \frac{1}{r}\in L_1(\mathbb…

Recently M. Kreck introduced a class of stratified spaces called p-stratifolds [M. Kreck, Stratifolds, Preprint]. He defined and investigated resolutions of p-stratifolds analogously to resolutions of algebraic varieties. In this note we…

In this paper, we deal with a singular quasilinear critical elliptic equation of Lichnerowicz type involving the p-Laplacian operator. With the help of the subcritical approach from variational method, we obtain the non-existence,…

We introduce Lorentz spaces $L_{p(\cdot),q}(\R^n)$ and $L_{p(\cdot),q(\cdot)}(\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity…

This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the…

This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a…

In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang…

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 investigate the $(k, m)$-constrained 1st modified Kadomtsev-Petviashvili (mKP) hierarchy $(L^k)_{\leq 0}= \sum_{i=1}^m q_i \partial^{-1} r_i \partial$. Here, we obtain the corresponding solutions in the form of generalized…

In the paper we generalize the notion of problem (P) introduced by Poletsky. We introduce the notion of (P_m) extremals. For example, geodesics are (P_1) extremals. Using obtained results we present a description of (P_m) extremals in…

Given $mp$ different $p$-planes in general position in $(m+p)$-dimensional space, a classical problem is to ask how many $p$-planes intersect all of them. For example when $m = p = 2$, this is precisely the question of "lines meeting four…

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an…

Several open problems concerning Minkowski endomorphisms and Minkowski valuations are solved. More precisely, it is proved that all Minkowski endomorphisms are uniformly continuous but that there exist Minkowski endomorphisms that are not…

We propose a generalized description for the kappa-Poincare-Hopf algebra as a symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are…

The general volume of a star body, a notion that includes the usual volume, the $q$th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that…

This work provides a detailed study of Meixner-Pollaczek polynomials and employs the central difference operator to study the Sturm-Liouville problem. It presents two linearly independent solutions to the recursion relation, along with the…

Existence and uniqueness in Minkowski space of entire downward translating solitons with prescribed values at infinity for a scalar curvature flow equation. The radial case translates into an ordinary differential equation and the general…

Let $C$ be a pointed closed convex cone in $\mathbb{R}^n$ with vertex at the origin $o$ and having nonempty interior. The set $A\subset C$ is $C$-coconvex if the volume of $A$ is finite and $A^{\bullet}=C\setminus A$ is a closed convex set.…