Harmonic Mappings of Riemannian Manifolds

1964 ◽  
Vol 86 (1) ◽  
pp. 109 ◽  
Author(s):  
James Eells ◽  
J. H. Sampson
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Mappings

HARMONIC MAPPINGS OF RIEMANNIAN MANIFOLDS.

Harmonic Maps ◽  
1992 ◽  
pp. 1-52
Author(s):  
JAMES EELLS ◽  
J. H. SAMPSON
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Mappings

Dirichlet's boundary value problem for harmonic mappings of Riemannian manifolds

1976 ◽  
Vol 147 (3) ◽  
pp. 225-236 ◽  
Author(s):  
Stefan Hildebrandt ◽  
Helmut Kaul ◽  
Kjell-Ove Widman
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Boundary Value ◽  
Harmonic Mappings

Interior estimates of harmonic heat flow

2021 ◽  
pp. 2150039
Author(s):  
Xiangao Liu ◽  
Zixuan Liu ◽  
Kui Wang
Keyword(s):  
Riemannian Manifolds ◽  
A Priori Estimates ◽  
A Priori ◽  
Regularity Result ◽  
Harmonic Mappings ◽  
Geodesic Ball ◽  
Priori Estimates ◽  
Schauder Estimate ◽  
Harmonic Flow ◽  
Harmonic Heat Flow

Motivated by Giaquinta and Hildebrandt’s regularity result for harmonic mappings [M. Giaquinta and S. Hildebrandt, A priori estimates for harmonic mappings, J. Reine Angew. Math. 1982(336) (1982) 124–164, Theorems 3 and 4], we show a [Formula: see text]-regularity result of the harmonic flow between two Riemannian manifolds when the image is in a regular geodesic ball. The proof is based on De Giorgi–Moser’s iteration and Schauder estimate.

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