Junjie Shan

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math.MG2026

The Discrete $L_{p}$ Minkowski Problem for Negative $p$

Junjie Shan

In this paper, we establish a homological existence criterion for the discrete $L_{p}$ Minkowski problem for all $p < 0$ , where $p = - n$ corresponds to the celebrated centro-affine case.…

math.MG2026

The Dual Minkowski Problem under Group Actions

Junjie Shan

In this paper, we study the dual Minkowski problem under group symmetry. For $0 < q \leq n$ , we give a complete existence characterization in the framework of $G$ -invariant convex bodi…

math.MG2025

The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies

Junjie Shan

In this paper, we study the $L_{p}$ dual Minkowski problem for all $q, p \in R$ from an algebraic perspective. We establish the existence of solutions for group-invariant co…

math.MG2025

The $L_{p}$ Gaussian Minkowski problem for $C$ -pseudo-cones

Junjie Shan, Wenchuan Hu

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 th…

math.MG2025

The Gaussian Minkowski-type problems for $C$ -pseudo-cones

Junjie Shan, Wenchuan Hu, Wenxue Xu

The Gaussian surface area measure and the Gaussian cone measure for $C$ -pseudo-cones are introduced and their corresponding Gaussian Minkowski problem and Gaussian log-Minkowski pr…

The Discrete Lp​ Minkowski Problem for Negative p

The Dual Minkowski Problem under Group Actions

The Lp​ Dual Minkowski Problem for Group-Invariant Convex Bodies

The Lp​ Gaussian Minkowski problem for C-pseudo-cones

The Gaussian Minkowski-type problems for C-pseudo-cones

The Discrete $L_{p}$ Minkowski Problem for Negative $p$

The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies

The $L_{p}$ Gaussian Minkowski problem for $C$ -pseudo-cones

The Gaussian Minkowski-type problems for $C$ -pseudo-cones