On the L dual Minkowski problem

By Yong Huang, Yiming Zhao. Advances in Mathematics, 2018

153 citations recorded by the source corpus.

Abstract The L p dual curvature measure was introduced by Lutwak, Yang & Zhang in an attempt to unify the L p Brunn–Minkowski theory and the dual Brunn–Minkowski theory. The characterization problem for L p dual curvature measure, called the L p dual Minkowski problem, is a fundamental problem in this unifying theory. The L p dual Minkowski problem contains the L p Minkowski problem and the dual Minkowski problem, two major problems in modern convex geometry that remain open in general. In this paper, existence results on the L p dual Minkowski problem in the weak sense will be provided. Moreover, existence and uniqueness of the solution in the smooth category will also be demonstrated.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/ffadaabb5913c8d867d56d524e8c72da6586937a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Haodi Chen
2. Qi-Rui Li
3. Shibing Chen
4. Yan-nan Liu
5. Jian Lu
6. Yiming Zhao
7. Yong Huang

In Astronomy and Astrophysics

1. Jian Lu
2. Haodi Chen
3. Shibing Chen
4. Qi-Rui Li
5. Yan-nan Liu

Citations in the corpus

• A flow method for the dual Orlicz–Minkowski problem (2020, methodology): “After the Lp dual Minkowski problem was first proposed in [57], several existence results of solutions were established in [4, 12, 35].”
• Variations of a class of Monge–Ampère-type functionals and their applications (2021, background): “3) was partially addressed in [6, 12, 14, 26], and the uniqueness of solutions was proved for p > q [26, 33].”
• The Lp dual Minkowski problem and related parabolic flows (2021, methodology): “The uniqueness and smoothness when f is positive and Cα or more regular were proved in [35].”
• The L dual Minkowski problem for p > 1 and q > 0 (2018, unknown): “ cases: • if p > q and µ is discrete (K is a polytope) according to Lutwak, Yang and Zhang [24], • if p > q, Q is a ball and µ has a Cα density function f for α ∈ (0,1] according to Huang, Zhao [19], • if p > 1, Q is a ball and q = n according to Hug, Lutwak, Yang, Zhang [16]. For Theorem 1”