Minimal discs in hyperbolic space bounded by a quasicircle at infinity
Minimal discs in hyperbolic space bounded by a quasicircle at infinity
复制标题
以无穷远拟圆为界的双曲空间中的最小圆盘
DOI：
10.4171/cmh/403
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Andrea Seppi
中科院分区：
文献类型：
--
作者：
Andrea Seppi
我们证明了双曲三维空间中最小嵌盘在无穷远边界上跨出一个准圆时，如果准圆足够接近于一个全测地平面的边界，则利用准圆在普适Teichmuller空间意义上的范数，以次线性的方式估计了该准圆的主曲率上值。作为一个副产品，我们证明了存在一个与格无关的普适常数C，使得如果拟fuchsian流形$M$两端之间的Teichmuller距离不超过C，则$M$几乎是fuchsian。证明的主要内容是极小曲面的凸包估计和控制主曲率的schauder型估计。
We prove that the supremum of principal curvatures of a minimal embedded disc in hyperbolic three-space spanning a quasicircle in the boundary at infinity is estimated in a sublinear way by the norm of the quasicircle in the sense of universal Teichmuller space, if the quasicircle is sufficiently close to being the boundary of a totally geodesic plane. As a by-product we prove that there is a universal constant C independent of the genus such that if the Teichmuller distance between the ends of a quasi-Fuchsian manifold $M$ is at most C, then $M$ is almost-Fuchsian. The main ingredients of the proofs are estimates on the convex hull of a minimal surface and Schauder-type estimates to control principal curvatures.
影响因子：
2.2
作者：
Fletcher A
通讯作者：
Fletcher A