Harmonic Mappings of Riemannian Manifolds

1964/01/01 by James Eells, J. H. Sampson · 174 citations
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry

paper · doi:10.2307/2373037

Cited by

• On the formation of singularities in the critical O (3) σ -model
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• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• On blow-up trees for the harmonic map heat flow from B² to S²
• Zeros of one-forms and the topology of algebraic maps
• Biconservative quasi-minimal immersions into semi-Euclidean spaces
• Computing discrete equivariant harmonic maps
• Biharmonic submanifolds with parallel mean curvature in\n mathbbSⁿ\×\ℝ
• Les applications conforme-harmoniques
• Gap theorems for Ricci-harmonic solitons
• New Geometric Flows on Riemannian Manifolds and Applications to Schrödinger-Airy Flows
• The Landau-Lifshitz equation of the ferromagnetic spin chain and Oseen-Frank flow
• An existence result of energy minimizer maps between riemannian polyhedra
• Classification results for biharmonic submanifolds in spheres
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• The motion of a random string
• Local existence of a fourth order dispersive curve flow on locally hermitian symmetric spaces and the application
• Explicit harmonic and wave maps into variable-curvature surfaces
• Equiaffine immersions and pseudo-Riemannian space forms
• On the gradient flows on Finsler manifolds
• The Weil-Petersson Geometry On the Thick Part of the Moduli Space of Riemann Surfaces
• Harmonic Self-maps of SU(3)
• The Classification of Biharmonic Curves of Cartan-Vranceanu 3-Dimensional Spaces
• Harmonic maps from S³ to S² and the rigidity of the Hopf fibration
• Uniqueness and nonuniqueness of limits of Teichmueller harmonic map flow
• Recent Developments on the Ricci Flow
• Harmonic maps into principal bundles and generalized magnetic maps
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• Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces
• Reduction methods for the bienergy
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• A note on biharmonic curves in Sasakian space forms
• On the biharmonic and harmonic indices of the Hopf map
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• Global regularity of wave maps III. Large energy from \R¹⁺² to hyperbolic spaces
• Nonclassical Lagrangian Dynamics and Potential Maps
• An Energy Reducing Flow for Multiple-Valued Functions
• A new parabolic flow in Kaehler manifolds
• On Deformable Minimal Hypersurfaces in Space Forms
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• Mean curvature flow into an ambient Riemannian manifold evolving by Ricci flow coupled with harmonic map heat flow
• Minimal surfaces with negative curvature in large dimensional spheres
• Uniqueness of 1D Generalized Bi-Schrödinger Flow
• Harmonic maps in singular geometry and rigidity
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• A survey on the optimal partition problem
• On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann Surfaces
• Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow
• Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
• Approximate solutions to the Dirichlet problem for harmonic maps between hyperbolic spaces
• Exotic structures and the limitations of certain analytic methods in geometry
• Geometric deformations of immersed surfaces in non-positively curved\n manifolds
• Classification of Weil-Petersson Isometries
• On geodesic homotopies of controlled width and conjugacies in isometry groups
• On uniqueness of heat flow of harmonic maps
• A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds
• Fibred K"ahler and quasi-projective Groups
• Weakly 1-completeness of holomorphic fiber bundles over compact Kähler manifolds
• Les Houches Lectures on Fields, Strings and Duality
• Proper Biconservative immersions into the Euclidean space
• Complete minimal submanifolds with nullity in Euclidean space
• Proper harmonic maps between asymptotically hyperbolic manifolds
• A conditional regularity result for p-harmonic flows
• HS-tensional maps and HM-tensional maps
• Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
• Saddle Point Configurations for Spherical Ferromagnets
• An optimal Loewner-type systolic inequality and harmonic one-forms of constant norm
• Weitzenböck-Bochner-Kodaira formulas with quadratic curvature terms
• The Cauchy problem for Schrodinger flows into Kahler manifolds
• A comparative study of finite element methods for a class of harmonic map heat flow problems
• A study of backward stochastic differential equation on a Riemannian manifold
• Harmonic maps between surfaces homotopic to a (branched) covering map
• Chen's conjecture on biharmonic submanifolds in Riemannian manifolds
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• BASIC STRUCTURAL EQUATIONS FOR ALMOST
\nRICCI-HARMONIC SOLITONS AND APPLICATIONS
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• Caculus of Variation and the L²-Bergman Metric on Teichmüller Space
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• Stable type II blowup for the 7 dimensional 1-corotational energy supercritical harmonic map heat flow
• The biharmonicity of sections of the tangent bundle
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• Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
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• Asymptotic flatness of the Weil-Petersson metric on Teichmuller space
• A Dirichlet problem on balls
• Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group
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• Biharmonic maps from tori into a 2-sphere
• Blow-up for the 3-dimensional axially symmetric harmonic map flow into\n S2
• Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
• Tangent spaces to the Teichmueller space from the energy-conscious perspective
• A short survey on biharmonic maps between Riemannian manifolds
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• Explicit formulas for biharmonic submanifolds in Sasakian space forms
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• Harmonic Mappings into non-negatively curved Riemannian manifolds
• Back to harmonic mappings of compact Riemannian manifolds
• Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
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• Global regularity of wave maps V. Large data local wellposedness and perturbation theory in the energy class
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• Pseudo-Harmonic Maps From Pseudo-Hermitian Manifolds to Riemannian Manifolds
• Surfaces in three-dimensional space forms with divergence-free stress-bienergy tensor
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• Biharmonic homomorphisms between Riemannian Lie groups
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• Limiting behaviour of the Ricci flow
• Expanding Ricci solitons and Higgs bundles
• Stability of the Morse Index for the p-harmonic Approximation of Harmonic Maps into Homogeneous Spaces
• Nonlinear Harmonic Forms and an Indefinite Bochner Formula
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• An algebraic description of screw dislocations in SC and BCC crystal lattices
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• Ricci flow [wikipedia]
• The heat flow for the full bosonic string. [europepmc]
• Refined asymptotics of the Teichmüller harmonic map flow into general targets. [europepmc]
• Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity. [europepmc]
• Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions. [europepmc]
• More Weakly Biharmonic Maps from the Ball to the Sphere. [europepmc]