A note on common zeroes of Laplace--Beltrami eigenfunctions

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dc.creatorGichev, V. M.
dc.date2005-11-28
dc.date.accessioned2026-07-07T06:51:50Z
dc.date.available2026-07-07T06:51:50Z
dc.descriptionLet $\De u+\la u=\De v+\la v=0$, where $\De$ is the Laplace--Beltrami operator on a compact connected smooth manifold $M$ and $\la>0$. If $H^1(M)=0$ then there exists $p\in M$ such that $u(p)=v(p)=0$. For homogeneous $M$, $H^1(M)\neq0$ implies the existence of a pair $u,v$ as above that has no common zero.
dc.description8 pages. This is the published paper with several additional comments in footnotes
dc.identifierhttps://arxiv.org/abs/math/0511688
dc.identifierhttp://arxiv.org/abs/math/0511688
dc.identifierAnnals of Global Anal. and Geom., 26 (2004), 201-208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105117
dc.subjectMetric Geometry
dc.subjectAnalysis of PDEs
dc.subject58J50
dc.titleA note on common zeroes of Laplace--Beltrami eigenfunctions
dc.typetext

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