An extremal eigenvalue problem in Kähler geometry

2014/11/28 by Apostolov, Vestislav, Jakobson, Dmitry, Kokarev, Gerasim
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.7725

Abstract

We study Laplace eigenvalues λ_k on Kähler manifolds as functionals on the space of Kähler metrics with cohomologous Kähler forms. We introduce a natural notion of a λ_k-extremal Kähler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the λ₁-extremal properties of Kähler-Einstein metrics of positive scalar curvature on manifolds with non-trivial holomorphic vector fields.

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