An extremal eigenvalue problem in K\"ahler geometry
Differential Geometry
2015-02-03 v2
Abstract
We study Laplace eigenvalues on K\"ahler manifolds as functionals on the space of K\"ahler metrics with cohomologous K\"ahler forms. We introduce a natural notion of a -extremal K\"ahler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the -extremal properties of K\"ahler-Einstein metrics of positive scalar curvature on manifolds with non-trivial holomorphic vector fields.
Cite
@article{arxiv.1411.7725,
title = {An extremal eigenvalue problem in K\"ahler geometry},
author = {Vestislav Apostolov and Dmitry Jakobson and Gerasim Kokarev},
journal= {arXiv preprint arXiv:1411.7725},
year = {2015}
}
Comments
Added references and a number of minor corrections. To appear in special issue of the Journal of Geometry and Physics