A geometric uncertainty principle with an application to Pleijel's estimate

Stefan Steinerberger

doi:10.1007/s00023-013-0310-4

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arXiv · 1306.3103

A geometric uncertainty principle with an application to Pleijel's estimate

Stefan Steinerberger

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Abstract

Consider partitions of an open, bounded domain in $\mathbb{R}^n$. Then an average element of the partition has either its Fraenkel asymmetry or its deviation from the smallest element in the partition bounded away from 0 by a universal constant. As an application, we give an (unspecified) improvement of Pleijel's estimate on the number of nodal domains of a Laplacian eigenfunction similar to recent work of Bourgain and improve a bound coming from spectral partition problems.

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BibTeX RIS

Stefan Steinerberger. 2013-11-04. A geometric uncertainty principle with an application to Pleijel's estimate. https://doi.org/10.1007/s00023-013-0310-4

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