An extremal eigenvalue problem in Kähler geometry
Journal of Geometry and Physics(2015)
摘要
We study Laplace eigenvalues λk on Kähler manifolds as functionals on the space of Kähler metrics with cohomologous Kähler forms. We introduce a natural notion of a λk-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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关键词
49R05,35P99,53C55,32Q20
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