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 Lp 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 Lp 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 p0.

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

CLC Number: 

  • 35K55
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