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The extrinsic polyharmonic map heat flow in the critical dimension
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Andreas Gastel
Veröffentlicht/Copyright:
16. Oktober 2006
Abstract
We consider the gradient flow of higher order elliptic functionals of the type ∫M
2 for maps from a compact Riemannian manifold M to ℝn with image contained in another compact manifold, called the extrinsic polyharmonic map heat flow. We prove that smooth initial values can be continued as an eternal solution to the flow if M is of dimension < 2m. In the critical case dim M = 2m, we find a unique eternal weak solution which is smooth except possibly for finitely many times. A singularity can occur only if a “bubble” separates, using up a certain amount of energy.
Received: 2004-09-30
Revised: 2005-05-09
Published Online: 2006-10-16
Published in Print: 2006-10-01
© Walter de Gruyter
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Artikel in diesem Heft
- On the critical points of a Riemannian surface
- The extrinsic polyharmonic map heat flow in the critical dimension
- Shult sets and translation ovoids of the Hermitian surface
- Classification of generalized polarized manifolds by their nef values
- Fano manifolds of coindex four as ample sections
- Groups generated by affine perspectivities
- Definability results for the Poisson equation
- Jung's theorem for a pair of Minkowski spaces
Artikel in diesem Heft
- On the critical points of a Riemannian surface
- The extrinsic polyharmonic map heat flow in the critical dimension
- Shult sets and translation ovoids of the Hermitian surface
- Classification of generalized polarized manifolds by their nef values
- Fano manifolds of coindex four as ample sections
- Groups generated by affine perspectivities
- Definability results for the Poisson equation
- Jung's theorem for a pair of Minkowski spaces
