Fundamental gap estimate for convex domains on sphere -- the case $n=2$

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 $D$ of sphere $S^{n}$ is $\geq 3 \frac{π^{2}}{D^{2}}$ when $n \geq 3 $. W e p r o v e t h e s a m e r e s u l t w h e n$ n=2$. In fact our proof works for all dimension. We also give an asymptotic expansion of the first and second Dirichlet eigenvalues of the model in [SWW16].

Fundamental gap estimate for convex domains on sphere -- the case $n = 2$

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Fundamental gap estimate for convex domains on sphere -- the case $n = 2$

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Fundamental gap estimate for convex domains on sphere -- the case n=2n=2

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Fundamental gap estimate for convex domains on sphere -- the case n=2n=2

文献摘要

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Fundamental gap estimate for convex domains on sphere -- the case $n = 2$

讲解博客

AI智能校验

Fundamental gap estimate for convex domains on sphere -- the case $n = 2$

讲解博客

AI智能校验