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

24 May 2020  ·  Bourni Theodora, Clutterbuck Julie, Nguyen Xuan Hien, Stancu Alina, Wei Guofang, Wheeler Valentina-Mira ·

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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Differential Geometry Analysis of PDEs