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

Yen Wen Fan, Ting Jung Kuo

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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.

Original languageEnglish
Pages (from-to)929-946
Number of pages18
JournalAsian Journal of Mathematics
Volume18
Issue number5
DOIs
Publication statusPublished - 2014 Jan 1

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Keywords

  • CR diameter
  • CR gradient estimate
  • Eigenvalue estimate
  • Sublaplacian

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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