Gauss curvature flow to the $L_p$-Gaussian chord Minkowski problem
Abstract
Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and $L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for $p=1$ and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. The smooth solution, up to now, to the $L_p$-Gaussian chord Minkowski problem is still open. Motivated by the forgoing works by Huang and Qin in \cite{HY01}, we propose in the present paper the $L_p(p>0)$-Gaussian chord Minkowski problem and log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to these two types of problems by the method of a Gauss curvature flow.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.05635
- arXiv:
- arXiv:2406.05635
- Bibcode:
- 2024arXiv240605635Z
- Keywords:
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- Mathematics - Differential Geometry;
- 52A20 \ \ 35K96\ \ 58J35
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:2404.19266