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On the Space of Kähler Potentials
Author(s) -
He Weiyong
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21515
Subject(s) - geodesic , mathematics , bounded function , manifold (fluid mechanics) , pure mathematics , space (punctuation) , kähler manifold , mathematical analysis , point (geometry) , geometry , linguistics , mechanical engineering , philosophy , engineering
We consider the geodesic equation for the generalized Kähler potential with only mixed second derivatives bounded. We show that given two such generalized Kähler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kähler potential has uniformly bounded mixed second derivatives (in manifold directions). This generalizes a fundamental theorem of Chen (2000) on the space of Kähler potentials.© 2014 Wiley Periodicals, Inc.