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Lower Bounds on Nodal Sets of Eigenfunctions via the Heat Flow by Steinerberger, Stefan is a scholarly article available to read on EtoBox.

What is Lower Bounds on Nodal Sets of Eigenfunctions via the Heat Flow about?

We study the size of nodal sets of Laplacian eigenfunctions on compact Riemannian manifolds without boundary and recover the currently optimal lower bound by comparing the heat flow of the eigenfunction with that of an artifically constructed diffusion process. The same method should apply to a number of other questions; for example, we prove a sharp result saying that a nodal domain cannot be entirely contained in a small neighbourhood of a 'reasonably flat' surface. We expect the arising concepts to have more connections to classical theory and pose some conjectures in that direction.

Author

Steinerberger, Stefan

Published

2013

Language

EN