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arXiv · 2005.11784

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
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Abstract

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.

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Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen, Alina Stancu, Guofang Wei, Valentina-Mira Wheeler. 2020-05-24. The vanishing of the fundamental gap of convex domains in $\mathbb H^n$. https://arxiv.org/abs/2005.11784

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