Prescribed $L_p$ quotient curvature problem and related eigenvalue problem

Xinqun Mei; Guofang Wang; Liangjun Weng

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arXiv · 2402.12314

Prescribed $L_p$ quotient curvature problem and related eigenvalue problem

Xinqun Mei·Guofang Wang·Liangjun Weng

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Abstract

In this paper, we investigate the existence of admissible (and strictly convex) smooth solutions to the prescribed $L_p$ quotient type curvature problem with $p>1$. For cases where $p=k-l+1$ and $p> k-l+1$, we obtain an admissible solution without any additional conditions, which is strictly spherically convex under a convexity condition. Under the same convexity condition, we establish the existence of a strictly spherically convex solution for the case $p<k-l+1$, provided that the prescribed function is even, a condition known to be necessary.

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Xinqun Mei, Guofang Wang, Liangjun Weng. 2024-02-19. Prescribed $L_p$ quotient curvature problem and related eigenvalue problem. https://arxiv.org/abs/2402.12314

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