In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap (the
difference between the first two eigenvalues) conjecture for convex domains in the …

The Vanishing of the Fundamental Gap of Convex Domains in $$\mathbb {H}^n$$ | Annales
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We study the log-concavity of the first Dirichlet eigenfunction of the Laplacian for convex
domains. For positively curved surfaces satisfying a condition involving the curvature and its …

S. Seto, L. Wang, and G. Wei proved that the gap between the first two Dirichlet eigenvalues
of a convex domain in the unit sphere is at least as large as that for an associated operator …

The fundamental gap of a domain is the difference between the first two eigenvalues of the
Laplace operator. In a series of recent and celebrated works, it was shown that for convex …

We provide a probabilistic proof of the fundamental gap estimate for Schrödinger operators
in convex domains on the sphere, which extends the probabilistic proof of F. Gong, H. Li …

Abstract We consider the Laplace–Beltrami operator with Dirichlet boundary conditions on
convex domains in a Riemannian manifold (M n, g) and prove that the product of the …

We obtain a fundamental gap estimate for classes of bounded domains with quantitative
control on the boundary in a complete manifold with integral bounds on the negative part of …

We show that, for horoconvex domains in the hyperbolic space, the product of their
fundamental gap with the square of their diameter has no positive lower bound. The result …

We establish sharp lower bounds for the first nonzero eigenvalue of the weighted p-
Laplacian with 1< p< ∞ 1< p<∞ on a compact Bakry–Émery manifold (M^ n, g, f)(M n, g, f) …