The vanishing of the fundamental gap of convex domains in $\mathbb H^n$

Alina Stancu; Guofang Wei; Julie Clutterbuck; Theodora Bourni; Valentina-Mira Wheeler; Xuan Hien Nguyen

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The vanishing of the fundamental gap of convex domains in mathbb H^n

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arxiv 2005.11784 v1 pith:UZDC72QQ submitted 2020-05-24 math.DG math.AP

The vanishing of the fundamental gap of convex domains in mathbb H^n

Theodora Bourni , Julie Clutterbuck , Xuan Hien Nguyen , Alina Stancu , Guofang Wei , Valentina-Mira Wheeler This is my paper

classification math.DG math.AP

keywords domainsconvexdiameterfundamentalmathbbarbitrarilyboundaryconditions

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For the Laplace operator with Dirichlet boundary conditions on convex domains in $\mathbb H^n$, $n\geq 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter.

The vanishing of the fundamental gap of convex domains in mathbb H^n

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