Boundary value problems for Dirac-harmonic maps and their heat flows

DOI10.1007/s10013-021-00484-wzbMath1472.53080OpenAlexW3144381239MaRDI QIDQ2042265

Miaomiao Zhu, Lei Liu

Publication date: 28 July 2021

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-021-00484-w

zbMATH Keywords

Dirac-harmonic mapDirichlet boundarychiral boundaryDirac-harmonic map flow\(\alpha\)-Dirac-harmonic map\(\alpha\)-Dirac-harmonic map flow

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20)

Cites Work

• Unnamed Item
• Dirac-harmonic maps from index theory
• The boundary value problem for the super-Liouville equation
• No neck for Dirac-harmonic maps
• Dirac-harmonic maps
• Energy identities for Dirac-harmonic maps
• Dirac-geodesics and their heat flows
• Some explicit constructions of Dirac-harmonic maps
• On the evolution of harmonic mappings of Riemannian surfaces
• The existence of minimal immersions of 2-spheres
• Finite-time blow-up of the heat flow of harmonic maps from surfaces
• Harmonic maps of manifolds with boundary
• Heat flow and boundary value problem for harmonic maps
• A global weak solution of the Dirac-harmonic map flow
• Short time existence of the heat flow for Dirac-harmonic maps on closed manifolds
• Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary
• Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem
• Eigenvalue boundary problems for the Dirac operator
• On singularities of the heat flow for harmonic maps from surfaces into spheres
• Energy identity for a class of approximate harmonic maps from surfaces
• The maximum principle and the Dirichlet problem for Dirac-harmonic maps
• The boundary value problem for Dirac-harmonic maps
• \( \alpha \)-Dirac-harmonic maps from closed surfaces
• Energy quantization for a singular super-Liouville boundary value problem
• Blow-up analysis for approximate Dirac-harmonic maps in dimension 2 with applications to the Dirac-harmonic heat flow
• The qualitative boundary behavior of blow-up solutions of the super-Liouville equations
• On the Sacks-Uhlenbeck flow of Riemannian surfaces
• Regularity theorems and energy identities for Dirac-harmonic maps
• A weak energy identity and the length of necks for a sequence of Sacks-Uhlenbeck \(\alpha \)-harmonic maps
• Bubbling of the heat flows for harmonic maps from surfaces
• Boundary Value Problems for Elliptic Differential Operators of First Order
• Harmonic Mappings of Riemannian Manifolds