Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (1): 161-179.doi: 10.1007/s10473-025-0113-y

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THE CHORD GAUSS CURVATURE FLOW AND ITS $ {L_{p}}$ CHORD MINKOWSKI PROBLEM

Jinrong Hu1,2, Yong Huang3, Jian Lu4, Sinan Wang5   

  1. 1. School of Mathematics, Hunan University, Changsha, 410082, Hunan Province, China;
    2. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria;
    3. School of Mathematics, Hunan University, Changsha 410082, China;
    4. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    5. School of Mathematics, Hunan University, Changsha 410082, China
  • Received:2024-09-01 Revised:2024-10-13 Published:2025-02-06
  • About author:Jinrong Hu, E-mail,: Hu_jinrong097@163.com; Yong Huang, E-mail,: huangyong@hnu.edu.cn; Jian Lu, E-mail,: lj-tshu04@163.com; Sinan Wang, E-mail,: wangsinan@hnu.edu.cn
  • Supported by:
    National Natural Science Foundation of China (12171144, 12231006, 12122106).

Abstract: In this paper, the $L_{p}$ chord Minkowski problem is concerned. Based on the results shown in [20], we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for $p>-n$ with $p\neq 0$.

Key words: $L_{p}$ chord Minkowski problem, new {M}onge-{A}mpère equation, geometric flow

CLC Number: 

  • 35K55
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