On the Geodesics in the space of Kähler metrics with prescribed singularities

Abstract

Motivated by the results of B. Berndtsson, in this memoir we use the new estimates developed by W. He to extend a theorem of the second author on the existence of weak $C^{1,1}$ geodesics between two smooth non-degenerate Kähler potentials to the case where the metrics on the end points may have singularities on some analytic set and may be positive semi-definite.

References in corpus (3)

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• Conical Kahler-Einstein metric revisited
• A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics

Cited by in corpus (1)

• The space of Kähler potentials on an asymptotically locally euclidean Kähler manifold