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Local Asymmetry and the Inner Radius of Nodal Domains

Dan Mangoubi
2008 Communications in Partial Differential Equations  

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2007 pre-print arXiv:math/0703663v1 fatcat:vztvt46c6necrjpc2ewcj33uau

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2008 accepted
arXiv:math/0703663v4 fatcat:xhtjtxs4a5ag3dicnxpxdggsl4
2007 pre-print
arXiv:math/0703663v3 fatcat:pbxoynwoinfqfg6vz34v5czs7y
2007 pre-print
arXiv:math/0703663v2 fatcat:cxtaqscjsvasnjqgbvns5y6lea
Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue λ. We show that the volume of f>0 inside any ball B whose center lies on f=0 is > C|B|/λ^n. We apply this result to prove that each nodal domain contains a ball of radius > C/λ^n.
doi:10.1080/03605300802038577 fatcat:tqst6kdydneiri3s73mbhd3pxa
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Dan Mangoubi. "Local Asymmetry and the Inner Radius of Nodal Domains." Communications in Partial Differential Equations 33.9 (2008) 1611-1621