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Author Hélein, Frédéric ♦ Hauswirth, Laurent ♦ Pacard, Frank
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-01-07
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Mathematical Physics ♦ Mathematics - Analysis of PDEs ♦ Mathematics - Differential Geometry ♦ 31A05 ♦ 35J25 ♦ 35R35 ♦ 49Q05 ♦ math ♦ physics:math-ph
Abstract We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the boundary. We study the two-dimensional case: we present various examples and give a general construction algorithm of such surface by using complex analysis. We deduce a classification of all such surfaces assuming some further natural hypotheses and prove a Bernstein type theorem.
Educational Use Research
Learning Resource Type Article