A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold
1994 ◽
Vol 56
(2)
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pp. 267-277
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AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.
2019 ◽
Vol 22
(5)
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pp. 1414-1436
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1977 ◽
Vol 77
(3-4)
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pp. 319-323
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2013 ◽
Vol 30
(6)
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pp. 983-996
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2012 ◽
Vol 24
(2)
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pp. 756-778
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