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Fundamental gaps of spherical triangles
Shoo Seto, Guofang Wei, Xuwen Zhu
We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical lunes and the spherical triangles which are half the lunes, and show that the fundamental gap goes to i…
The first nonzero eigenvalue of the -Laplacian on Differential forms
Shoo Seto
we introduce a generalization of the -Laplace operator to act on differential forms and generalize an estimate of Gallot-Meyer for the first nonzero eigenvalue on closed Riemann…
Zhong-Yang type eigenvalue estimate with integral curvature condition
Xavier Ramos Olivé, Shoo Seto, Guofang Wei +1
We prove a sharp Zhong-Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature.
First eigenvalue of the -Laplacian on Kähler manifolds
Casey Blacker, Shoo Seto
We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the -Laplacian on Kähler manifolds. Parallel to the case, the first eigenvalue lower boun…
Fundamental gap estimate for convex domains on sphere -- the case
Xianzhe Dai, Shoo Seto, Guofang Wei
In [SWW16, HW17] it is shown that the difference of the first two eigenvalues of the Laplacian with Dirichlet boundary condition on convex domain with diameter of sphere $\math…
First eigenvalue of the -Laplacian under integral curvature condition
Shoo Seto, Guofang Wei
We give various estimates of the first eigenvalue of the -Laplace operator on closed Riemannian manifold with integral curvature conditions.