An extremal eigenvalue problem in Kähler geometry

Abstract

We study Laplace eigenvalues ${\lambda }_k$ on Kähler manifolds as functionals on the space of Kähler metrics with cohomologous Kähler forms. We introduce a natural notion of a ${\lambda }_k$-extremal Kähler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the ${\lambda }_1$-extremal properties of Kähler-Einstein metrics of positive scalar curvature on manifolds with non-trivial holomorphic vector fields.

Added references and a number of minor corrections. To appear in special issue of the Journal of Geometry and Physics

References in corpus (2)

• K-stability and Kähler-Einstein metrics
• Kahler-Einstein metrics and stability