The intrinsic geometry of a Jordan domain
Richard L. Bishop
Abstract
For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a CAT(0)space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.
Create a lesson
Related papers
Scalar curvature on Kähler blow-ups and systolic inequalities
Zehao Sha, Jian Wang
Strict Stability and Strict Minimality of Regular Area-Minimizing Hypercones: A Quantitative Characterization
Gongping Niu
Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs
Arunima Bhattacharya, Gerard Orriols, Anna Skorobogatova
Torus actions, almost non-negative curvature and fundamental groups
Michael Wiemeler
Optimal Transport and the ABP Method in Higher Codimension
Bang-Xian Han, Zhe-Feng Xu
An isoperimetric characterization of a new ADM-like mass for C0-asymptotically flat manifolds
Luca Benatti, Mattia Fogagnolo