دورية أكاديمية
A flow approach to the prescribed Gaussian curvature problem in ℍ푛+1.
| العنوان: | A flow approach to the prescribed Gaussian curvature problem in ℍ푛+1. |
|---|---|
| المؤلفون: | Li, Haizhong, Zhang, Ruijia |
| المصدر: | Advances in Calculus of Variations; Jul2024, Vol. 17 Issue 3, p521-543, 23p |
| مصطلحات موضوعية: | GAUSSIAN curvature, SMOOTHNESS of functions, HYPERBOLIC spaces, HYPERSURFACES, EQUATIONS, GENERALIZATION |
| مستخلص: | In this paper, we study the following prescribed Gaussian curvature problem: K = f ~ (θ) ϕ (ρ) α − 2 ϕ (ρ) 2 + | ∇ ¯ ρ | 2 , a generalization of the Alexandrov problem ( α = n + 1 ) in hyperbolic space, where f ~ is a smooth positive function on S n , 휌 is the radial function of the hypersurface, ϕ (ρ) = sinh ρ and 퐾 is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when α ≥ n + 1 . Our argument provides a parabolic proof in smooth category for the Alexandrov problem in H n + 1 . We also consider the cases 2 < α ≤ n + 1 under the evenness assumption of f ~ and prove the existence of solutions to the above equations. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances in Calculus of Variations is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| قاعدة البيانات: | Complementary Index |
كن أول من يترك تعليقا!