scholarly journals Regularity and Blow-Up Analysis for J-Holomorphic Maps

2003 ◽  
Vol 05 (04) ◽  
pp. 671-704
Author(s):  
Changyou Wang
Keyword(s):  
Blow Up ◽  
Harmonic Maps ◽  
Hermitian Manifold ◽  
Singular Set ◽  
Holomorphic Maps ◽  
Almost Hermitian Manifold ◽  
Holomorphic Map ◽  
Energy Quantization ◽  
Blow Up Analysis ◽  
Almost Kähler

If u∈H1(M,N) is a weakly J-holomorphic map from a compact without boundary almost hermitian manifold (M,j,g) into another compact without boundary almost hermitian manifold (N,J,h). Then it is smooth near any point x where Du has vanishing Morrey norm ℳ2,2m-2, with 2m= dim (M). Hence H2m-2measure of the singular set for a stationary J-holomorphic map is zero. Blow-up analysis and the energy quantization theorem are established for stationary J-holomorphic maps. Connections between stationary J-holomorphic maps and stationary harmonic maps are given for either almost Kähler manifolds M and N or symmetric ∇hJ.

Blow-Up Analysis for Heat Flow of Harmonic Maps

Nematics ◽  
1991 ◽  
pp. 49-64
Author(s):  
Chen Yunmei ◽  
Ding Wei-Yue
Keyword(s):  
Heat Flow ◽  
Blow Up ◽  
Harmonic Maps ◽  
Blow Up Analysis

scholarly journals RC-POSITIVITY, VANISHING THEOREMS AND RIGIDITY OF HOLOMORPHIC MAPS

2019 ◽  
pp. 1-16
Author(s):  
Xiaokui Yang
Keyword(s):  
Complex Manifold ◽  
Hermitian Manifold ◽  
Compact Complex Manifold ◽  
Holomorphic Sectional Curvature ◽  
Vanishing Theorems ◽  
Holomorphic Maps ◽  
Holomorphic Map ◽  
Holomorphic Bisectional Curvature ◽  
Tautological Line Bundle ◽  
Compact Complex Manifolds

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle ${\mathcal{O}}_{T_{M}^{\ast }}(1)$ is not pseudo-effective and ${\mathcal{O}}_{T_{N}^{\ast }}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$ . In particular, we prove that any holomorphic map from a compact complex manifold $M$ with RC-positive tangent bundle to a compact complex manifold $N$ with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.

A SCHWARZ LEMMA FOR -HARMONIC MAPS AND THEIR APPLICATIONS

2017 ◽  
Vol 96 (3) ◽  
pp. 504-512 ◽  
Author(s):  
QUN CHEN ◽  
GUANGWEN ZHAO
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Schwarz Lemma ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Almost Kähler

We establish a Schwarz lemma for $V$-harmonic maps of generalised dilatation between Riemannian manifolds. We apply the result to obtain corresponding results for Weyl harmonic maps of generalised dilatation from conformal Weyl manifolds to Riemannian manifolds and holomorphic maps from almost Hermitian manifolds to quasi-Kähler and almost Kähler manifolds.

ON SACKS–UHLENBECK'S EXISTENCE THEOREM FOR HARMONIC MAPS VIA EXPONENTIALLY HARMONIC MAPS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250105 ◽  
Author(s):  
TOSHIAKI OMORI
Keyword(s):  
Existence Theorem ◽  
Homotopy Class ◽  
Existence Result ◽  
Blow Up ◽  
Harmonic Maps ◽  
Closed Surface ◽  
Closed Manifold ◽  
Blow Up Analysis

The blow-up analysis for a sequence of exponentially harmonic maps from a closed surface is studied to reestablish an existence result of harmonic maps from a closed surface into a closed manifold whose 2-dimensional homotopy class vanishes.

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