Related papers: The Minkowski problem in the Gaussian probability …
This article delves into the $L_p$ Minkowski problem within the framework of generalized Gaussian probability space. This type of probability space was initially introduced in information theory through the seminal works of Lutwak, Yang,…
In this paper, we extend the article that Minkowski problem in Gaussian probability space of Huang et al. to $L_p$-Gaussian Minkowski problem, and obtain the existence and uniqueness of $o$-symmetry weak solution in case of $p\geq1$.
The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.
In this paper, we derive the existence of solutions with small volume to the $L_p$-Gaussian Minkowski problem for $1\leq p<n$, which implies that there are at least two solutions for the $L_p$-Gaussian Minkowski problem.
Existence of symmetric (resp. asymmetric) solutions to the $L_p$ Gaussian Minkowski problem for $p\leq 0$ (resp. $p\geq 1$) will be provided. Moreover, existence and uniqueness of smooth solutions to the problem for $p>n$ will also be…
In this paper, we study the $L_p$-Gaussian Minkowski problem, which arises in the $L_p$-Brunn-Minkowski theory in Gaussian probability space. We use Aleksandrov's variational method with Lagrange multipliers to prove the existence of the…
In this paper, we study the anisotropic Minkowski problem. It is a problem of prescribing the anisotropic Gauss-Kronecker curvature for a closed strongly convex hypersurface in Euclidean space as a function on its anisotropic normals in…
The $L_{p}$ Gaussian Minkowski problem for $C$-pseudo-cones is studied in this paper, and the existence and uniqueness results are established. This extends our previous work on the Minkowski problem for $C$-pseudo-cones with respect to the…
The existence of solutions to the Gaussian logarithmic Minkowski problem for C-pseudo-cones is established in this paper. In addition, the non-uniqueness of solutions to the problem is demonstrated.
The uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem in $\mathbb{R}^{n+1}$ is established when $-(n+1)<p<-1$ with $n\geq 1$, without requiring the origin-centred assumption on convex bodies.
Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.
The even Gaussian dual Minkowski problem studied by Feng, Hu and Xu, In this paper, we consider the even $L_p$ dual-Gaussian Minkowski problem for $p>1$. The existence of $o$-symmetric solution in the case $p>1$ is obtained.
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image…
The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a…
As we all know, the Minkowski type problem is the cornerstone of the Brunn-Minkowski theory in Euclidean space. The Heisenberg group as a sub-Riemannian space is the simplest non-Abelian degenerate Riemannian space that is completely…
The dual $L_p$-Minkowski problem with $p<0<q$ is investigated in this paper. By proving a new existence result of solutions and constructing an example, we obtain the non-uniqueness of solutions to this problem.
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an…
This paper gives a systematic study to the general dual-polar Orlicz-Minkowski problem (e.g., Problem \ref{general-dual-polar}). This problem involves the general dual volume $\widetilde{V}_G(\cdot)$ recently proposed in \cite{GHWXY, GHXY}…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
The Gaussian surface area measures for $C$-pseudo-cones are studied in this paper. Using the variational arguments and the approximation methods of Schneider, we obtain the existence of solutions to the Gaussian-Minkowski problem for…