Matzoh ball soup in spaces of constant curvature

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dc.creatorLiu, Genqian
dc.date2008-07-26
dc.date.accessioned2026-07-07T09:53:08Z
dc.date.available2026-07-07T09:53:08Z
dc.descriptionIn this paper, we generalize Magnanini-Sakaguchi's result [MS3] from Euclidean space to spaces of constant curvature. More precisely, we show that if a conductor satisfying the exterior geodesic sphere condition in the space of constant curvature has initial temperature 0 and its boundary is kept at temperature 1 (at all times), if the thermal conductivity of the conductor is inverse of its metric, and if the conductor contains a proper sub-domain, satisfying the interior geodesic cone condition and having constant boundary temperature at each given time, then the conductor must be a geodesic ball. Moreover, we show similar result for the wave equations and the Schrödinger equations in spaces of constant curvature.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0807.4213
dc.identifierhttp://arxiv.org/abs/0807.4213
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165845
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35K05, 35K20, 35J05, 58J35, 35J10
dc.titleMatzoh ball soup in spaces of constant curvature
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