Relative energy gap for harmonic maps of riemann surfaces into real analytic riemannian manifolds

Paul M.N. Feehan

doi:10.1090/proc/14013

Relative energy gap for harmonic maps of riemann surfaces into real analytic riemannian manifolds

Paul M.N. Feehan

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We extend the well-known Sacks-Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.

Original language	English (US)
Pages (from-to)	3179-3190
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	7
DOIs	https://doi.org/10.1090/proc/14013
State	Published - Jul 2018

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Harmonic maps
Łojasiewicz-Simon gradient inequality

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10.1090/proc/14013

Cite this

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title = "Relative energy gap for harmonic maps of riemann surfaces into real analytic riemannian manifolds",

abstract = "We extend the well-known Sacks-Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.",

keywords = "Harmonic maps, {\L}ojasiewicz-Simon gradient inequality",

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note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

month = jul,

doi = "10.1090/proc/14013",

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AU - Feehan, Paul M.N.

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N2 - We extend the well-known Sacks-Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.

AB - We extend the well-known Sacks-Uhlenbeck energy gap result for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic map.

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KW - Łojasiewicz-Simon gradient inequality

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JO - Proceedings of the American Mathematical Society

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Relative energy gap for harmonic maps of riemann surfaces into real analytic riemannian manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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