Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 223, Issue 3, Pages 1123-1182Publisher
SPRINGER
DOI: 10.1007/s00205-016-1054-3
Keywords
-
Categories
Funding
- Swiss National Science Foundation [153599]
Ask authors/readers for more resources
We solve the classical problem of Plateau in the setting of proper metric spaces. Precisely, we prove that among all disc-type surfaces with prescribed Jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi-conformal parametrization. If the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally Holder continuous in the interior and continuous up to the boundary. Our results generalize corresponding results of Douglas Rad and Morrey from the setting of Euclidean space and Riemannian manifolds to that of proper metric spaces.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available