On the estimate of first positive eigenvalue of a sublaplacian in a pseudohermitian manifold

Yen Wen Fan; Ting Jung Kuo

doi:10.4310/AJM.2014.v18.n5.a7

On the estimate of first positive eigenvalue of a sublaplacian in a pseudohermitian manifold

Yen Wen Fan
, Ting Jung Kuo

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we first obtain a CR version of Yau's gradient estimate for eigenfunc- tions of a sublaplacian. Second, by using CR analogue of Li-Yau's eigenvalue estimate, we are able to obtain a lower bound of the first positive eigenvalue in a pseudohermitian manifold of nonvanishing pseudohermitian torsion and nonpositive lower bound on pseudohermitian Ricci curvature.

Original language	English
Pages (from-to)	929-946
Number of pages	18
Journal	Asian Journal of Mathematics
Volume	18
Issue number	5
DOIs	https://doi.org/10.4310/AJM.2014.v18.n5.a7
Publication status	Published - 2014
Externally published	Yes

Keywords

CR diameter
CR gradient estimate
Eigenvalue estimate
Sublaplacian

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4310/AJM.2014.v18.n5.a7

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abstract = "In this paper, we first obtain a CR version of Yau's gradient estimate for eigenfunc- tions of a sublaplacian. Second, by using CR analogue of Li-Yau's eigenvalue estimate, we are able to obtain a lower bound of the first positive eigenvalue in a pseudohermitian manifold of nonvanishing pseudohermitian torsion and nonpositive lower bound on pseudohermitian Ricci curvature.",

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AU - Kuo, Ting Jung

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AB - In this paper, we first obtain a CR version of Yau's gradient estimate for eigenfunc- tions of a sublaplacian. Second, by using CR analogue of Li-Yau's eigenvalue estimate, we are able to obtain a lower bound of the first positive eigenvalue in a pseudohermitian manifold of nonvanishing pseudohermitian torsion and nonpositive lower bound on pseudohermitian Ricci curvature.

KW - CR diameter

KW - CR gradient estimate

KW - Eigenvalue estimate

KW - Sublaplacian

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JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 5

ER -

On the estimate of first positive eigenvalue of a sublaplacian in a pseudohermitian manifold

Abstract

Keywords

ASJC Scopus subject areas

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