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• W3100647802 abstract "We use tools from $n$-dimensional Brownian motion in conjunction with the Feynman-Kac formulation of heat diffusion to study nodal geometry on a compact Riemannian manifold $M$. On one hand we extend a theorem of Lieb and prove that any nodal domain $Omega_lambda$ almost fully contains a ball of radius $sim frac{1}{sqrt{lambda}}$. This also gives a slight refinement of a result by Mangoubi, concerning the inradius of nodal domains (cite{Man2}). On the other hand, we also prove that no nodal domain can be contained in a reasonably thin tubular neighbourhood of unions of finitely many surfaces inside $M$." @default.
• W3100647802 created "2020-11-23" @default.
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• W3100647802 date "2018-01-01" @default.
• W3100647802 modified "2023-09-24" @default.
• W3100647802 title "Nodal geometry, heat diffusion and Brownian motion" @default.
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• W3100647802 doi "https://doi.org/10.2140/apde.2018.11.133" @default.
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