Removability of the singular set of the heat flow of harmonic maps

Chen, Yunmei; Flaminio, Livio

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1090/S0002-9939-96-03169-3

Title :

Removability of the singular set of the heat flow of harmonic maps

Author(s) :

Chen, Yunmei [Auteur]
Department of Mathematics [Gainesville] [UF|Math]
Flaminio, Livio [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Proceedings of the American Mathematical Society

Pages :

513-525

Publisher :

American Mathematical Society

Publication date :

1996

ISSN :

0002-9939

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

<p>We show that the singular set of a weak stationary solution <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u"> <mml:semantics> <mml:mi>u</mml:mi> <mml:annotation ...
Show more ><p>We show that the singular set of a weak stationary solution <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u"> <mml:semantics> <mml:mi>u</mml:mi> <mml:annotation encoding="application/x-tex">u</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the heat flow of harmonic maps between Riemannian manifolds <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact, is removable if it has “parabolic codimension” greater than two and the initial energy <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E left-parenthesis u 0 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>u</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">E(u_0)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is sufficiently small.</p>Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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