Geodesic Convexity of Small Neighborhood in the Space of Kähler Potentials
Abstract
We show that, given $k> 4$, $0<J<\min\{{1\over 4},{k-4\over 4}\}$, any point in space of non-degenerate smooth Kähler potentials has a small neighborhood with respect to $C^k$ norm, s.t. any two points in this neighborhood can be connected by a geodesic of at least $C^{k-J}$ regularity.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2018
- DOI:
- 10.48550/arXiv.1805.02373
- arXiv:
- arXiv:1805.02373
- Bibcode:
- 2018arXiv180502373C
- Keywords:
-
- Mathematics - Analysis of PDEs;
- 35H20;
- 35R35;
- 58C15;
- 53C55
- E-Print:
- 55 pages