On Stekloff eigenvalue problem

Roger Chen, Chiung Jue Sung

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let (Mn, g) be a smooth compact Riemannian manifold with boundary ∂M ≠ 0. In this article we discuss the first positive eigenvalue of the Stekloff eigenvalue problem {(-Δ + q)u(x) = 0 in M ∂u/∂v = λu on ∂M, where q(x) is a C2 function defined on M, ∂vg is the normal derivative with respect to the unit outward normal vector on the boundary ∂M. In particular, when the boundary ∂M satisfies the "interior rolling R-ball" condition, we obtain a positive lower bound for the first nonzero eigenvalue in terms of n, the diameter of M, R, the lower bound of the Ricci curvature, the lower bound of the second fundamental form elements, and the tangential derivatives of the second fundamental form elements.

Original languageEnglish
Pages (from-to)277-296
Number of pages20
JournalPacific Journal of Mathematics
Issue number2
Publication statusPublished - 2000 Oct

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'On Stekloff eigenvalue problem'. Together they form a unique fingerprint.

Cite this