Related papers: The Lp Minkowski problem for polytopes for negativ…
Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.
Necessary and sufficient conditions for the existence of solutions to the asymmetric $L_p$ Minkowski problem in $\mathbb{R}^2$ are established for $0 < p < 1$.
An Orlicz version of the $L_p$-Minkowski problem on $S^{n-1}$ is discussed corresponding to the case $-n<p<0$.
The $L_p$-Minkowski problem deals with the existence of closed convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed $p$-area measures. It extends the classical Minkowski problem and embraces several important geometric and physical…
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.
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 current state of art concerning the $L_p$ Minkowski problem as a Monge-Ampere equation on the sphere and Lutwak's Logarithmic Minkowski conjecture about the uniqueness of even solution in the $p=0$ case are surveyed and connections to…
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.
In this paper, we solve the $L_p$ chord Minkowski problem in the case of discrete measures whose supports are in general position for negative $p$ and $q>0.$ As for general Borel measure with a density, we also give a proof but need…
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 $p\geq1$.
In this paper, we study the planar Lp-Minkowski problem for all p, which was introduced by Lutwak [23]. A detailed exploration on solvability and uniqueness will be presented.
This paper explores the nonuniqueness of solutions to the $L_p$ chord Minkowski problem for negative $p.$ The $L_p$ chord Minkowski problem was recently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and…
In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby…
In this paper, we consider the Minkowski problem associated with the solution to the anisotropic $p$-Laplacian (or Finsler $p$-Laplacian) equation, namely, the Minkowski problem of anisotropic $p$-torsional rigidity. The sufficient and…
The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem for…
In this paper, {we extend the affine dual curvature measures to the $L_p$ setting and solve the existence part of the corresponding Minkowski problem for non-symmetric discrete measures when $p>1$ and for symmetric measures when $p\geq0$.}…
In this paper, the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity is considered. The existence of the solution of the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity with $0<q<1$ and $1<q\neq \frac{p}{p-1}+n$ is…
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.
Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p \geq 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and…
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…