A structure theorem for polyharmonic maps between Riemannian manifolds

被引：14

作者：

Branding, Volker ^{[1
]}

机构：

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 273卷

基金：

奥地利科学基金会;

关键词：

Polyharmonic maps; Harmonic maps; Classification result; K-ENERGY;

D O I：

10.1016/j.jde.2020.11.046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that polyharmonic maps of arbitrary order from complete nonparabolic Riemannian manifolds to arbitrary Riemannian manifolds must be harmonic if certain smallness and integrability conditions hold. (C) 2020 The Author(s). Published by Elsevier Inc.

引用

页码：14 / 39

页数：26

共 18 条

[1] Higher order energy functionals [J].

Branding, V ;

Montaldo, S. ;

Oniciuc, C. ;

Ratto, A. .

ADVANCES IN MATHEMATICS, 2020, 370

[2] A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds [J].

Branding, Volker ;

Luo, Yong .

JOURNAL OF GEOMETRY AND PHYSICS, 2020, 148

[3] A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions [J].

Branding, Volker .

JOURNAL OF GEOMETRY AND PHYSICS, 2018, 134 :1-10

[4] A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies [J].

Branding, Volker .

ARCHIV DER MATHEMATIK, 2018, 111 (03) :329-336

[5] Global existence of Dirac-wave maps with curvature term on expanding spacetimes [J].

Branding, Volker ;

Kroencke, Klaus .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (05) :1-30

[6] A SPECIAL STOKES THEOREM FOR COMPLETE RIEMANNIAN MANIFOLDS [J].

GAFFNEY, MP .

ANNALS OF MATHEMATICS, 1954, 60 (01) :140-145

[7]

Gastel A, 2009, COMMUN ANAL GEOM, V17, P185

[8] On polyharmonic maps into spheres in the critical dimension [J].

Goldstein, Pawel ;

Strzelecki, Pawel ;

Zatorska-Goldstein, Anna .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (04) :1387-1405

[9]

Maeta S, 2012, BALK J GEOM APPL, V17, P70

[10] Triharmonic isometric immersions into a manifold of non-positively constant curvature [J].

Maeta, Shun ;

Nakauchi, Nobumitsu ;

Urakawa, Hajime .

MONATSHEFTE FUR MATHEMATIK, 2015, 177 (04) :551-567

← 1 2 →