Sudan Xing

activity

20172026

most citedOn

L_{p}

-Brunn-Minkowski type and

L_{p}

-isoperimetric type inequalities for general measures

2 citations · 6 across the 11 of their papers we have counts for

collaborators

11 papers

math.FA2026

Fixed Point Rigidity of the Operator $Γ_{p} Π_{p}^{*}$ and the LYZ Conjecture

Youjiang Lin, Sudan Xing

We characterize the fixed points of the operator $Γ_{p} Π_{p}^{*}$ for $n \geq 3$ and $1 < p < n$ . More precisely, we prove that a convex body $K \in K_{o}^{n}$ satisfies \[Γ_pΠ_p^\ast K…

math.FA2022

On Multiple $L_{p}$ -curvilinear-Brunn-Minkowski inequalities

Michael Roysdon, Sudan Xing

We construct the extension of the curvilinear summation for bounded Borel measurable sets to the $L_{p}$ space for multiple power parameter $α ˉ = (α_{1}, \dots, α_{n + 1})$ when $p > 0$ .…

math.FA2021

On the framework of $L_{p}$ summations for functions

Michae Roysdon, Sudan Xing

We develop the framework of $L_{p}$ operations for functions by introducing two primary new types $L_{p, s}$ summations for $p > 0$ : the $L_{p, s}$ convolution sum and the $L_{p, s}$ Aspl…

math.MG2021★ 1 cited

On the Musielak-Orlicz-Gauss image problem

Qingzhong Huang, Sudan Xing, Deping Ye +1

In the present paper we initiate the study of the Musielak-Orlicz-Brunn-Minkowski theory for convex bodies. In particular, we develop the Musielak-Orlicz-Gauss image problem aiming…

math.FA2020★ 1 cited

Geometry of log-concave functions: the $L_{p}$ Asplund sum and the $L_{p}$ Minkowski problem

Niufa Fang, Sudan Xing, Deping Ye

The aim of this paper is to develop a basic framework of the $L_{p}$ theory for the geometry of log-concave functions, which can be viewed as a functional "lifting" of the $L_{p}$ Brun…

math.FA2020★ 2 cited

On $L_{p}$ -Brunn-Minkowski type and $L_{p}$ -isoperimetric type inequalities for general measures

Michael Roysdon, Sudan Xing

In 2011 Lutwak, Yang and Zhang extended the definition of the $L_{p}$ -Minkowski convex combination ( $p \geq 1$ ) introduced by Firey in the 1960s from convex bodies containing the ori…

math.MG2019

The general dual-polar Orlicz-Minkowski problem

Sudan Xing, Deping Ye, Baocheng Zhu

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 $\wid…

math.MG2018

General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II

Richard J. Gardner, Daniel Hug, Sudan Xing +1

The general dual volume $\dveV(K)$ and the general dual Orlicz curvature measure $\deV(K, \cdot)$ were recently introduced for functions $G: (0, \infty)\times \sphere\rightarrow (0…

math.MG2018

General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I

Richard J. Gardner, Daniel Hug, Wolfgang Weil +2

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 ne…

math.MG2018★ 1 cited

On the general dual Orlicz-Minkowski problem

Sudan Xing, Deping Ye

For $K \subseteq R^{n}$ a convex body with the origin $o$ in its interior, and $ϕ : R^{n} ∖ {o} \to (0, \infty)$ a continuous function, define the general…

math.MG2017★ 1 cited

The dual Orlicz-Minkowski problem

Baocheng Zhu, Sudan Xing, Deping Ye

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in ord…