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- W4221139149 abstract "In this paper, we study the following prescribed Gaussian curvature problem $$K=frac{tilde{f}(theta)}{phi(rho)^{alpha-2}sqrt{phi(rho)^2+|bar{nabla}rho|^2}},$$ a generalization of the Alexandrov problem ($alpha=n+1$) in hyperbolic space, where $tilde{f}$ is a smooth positive function on $mathbb{S}^{n}$, $rho$ is the radial function of the hypersurface, $phi(rho)=sinhrho$ and $K$ is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when $alphageq n+1$. Our argument provides a parabolic proof in smooth category for the Alexandrov problem in $mathbb{H}^{n+1}$. We also consider the cases $2<alphaleq n+1$ under the evenness assumption of $tilde{f}$ and prove the existence of solutions to the above equations." @default.
- W4221139149 created "2022-04-03" @default.
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- W4221139149 date "2022-03-28" @default.
- W4221139149 modified "2023-09-24" @default.
- W4221139149 title "A flow approach to the prescribed Gaussian curvature problem in $mathbb{H}^{n+1}$" @default.
- W4221139149 doi "https://doi.org/10.48550/arxiv.2203.14594" @default.
- W4221139149 hasPublicationYear "2022" @default.
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