THE LP DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$

doi:10.1007/s10473-026-0209-z

数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (2): 697-713.doi: 10.1007/s10473-026-0209-z

THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$

Ni Xiang, Yuni Xiong^*

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

收稿日期:2024-11-11 修回日期:2025-04-07 发布日期:2026-05-22

THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$

Ni Xiang, Yuni Xiong^*

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

Received:2024-11-11 Revised:2025-04-07 Published:2026-05-22
Contact: ^*Xiong,E-mail: 202121104011767@stu.hubu.edu.cn
About author:Ni Xiang,E-mail: nixiang@hubu.edu.cn
Supported by:
Xiang's research was supported by the NSFC (11971157, 12426532, 2571213).

摘要/Abstract

摘要： In this paper, we establish the {\it a priori} estimates for solutions of mixed Hessian quotient type equations on $\mathbb{S}^n$. Then we obtain the existence and uniqueness of $\widetilde{\Gamma}_k$-admissible solutions to the $L_p$ dual Minkowski type problem with $p\geq q$. Moreover, we show the existence of convex solutions by Constant Rank Theorem.

关键词: $L_p$ dual Minkowski type problems, $\widetilde{\Gamma}_k$-admissible solutions, convex solutions

Abstract: In this paper, we establish the {\it a priori} estimates for solutions of mixed Hessian quotient type equations on $\mathbb{S}^n$. Then we obtain the existence and uniqueness of $\widetilde{\Gamma}_k$-admissible solutions to the $L_p$ dual Minkowski type problem with $p\geq q$. Moreover, we show the existence of convex solutions by Constant Rank Theorem.

Key words: $L_p$ dual Minkowski type problems, $\widetilde{\Gamma}_k$-admissible solutions, convex solutions

中图分类号:

35J60

Ni Xiang, Yuni Xiong. THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$[J]. 数学物理学报(英文版), 2026, 46(2): 697-713.

Ni Xiang, Yuni Xiong. THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$[J]. Acta mathematica scientia,Series B, 2026, 46(2): 697-713.

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THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$

THE L_P DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$

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