The nonexistence of stable submanifolds, varifolds, and harmonic maps in sufficiently pinched simply connected Riemannian manifolds

DOI10.1307/MMJ/1029003241zbMath0591.49030OpenAlexW2037373074WikidataQ115239006 ScholiaQ115239006MaRDI QIDQ1074856

Ralph Howard

Publication date: 1985

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1029003241

zbMATH Keywords

harmonic mapsintegral currentsvarifoldspinched Riemannian manifoldstable p-dimensional submanifolds

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Potential theory on Riemannian manifolds and other spaces (31C12) Currents in global analysis (58A25)

Related Items (13)

On the Gehring link problem and the isoperimetric inequality of Bombieri and Simon ⋮ On stable quasi-harmonic maps and Liouville type theorems ⋮ Instability of spheres with deformed Riemannian metrics ⋮ On the instability of minimal submanifolds in Riemannian manifolds of positive curvature ⋮ Stable harmonic maps from pinched manifolds ⋮ Pinching and nonexistence of stable harmonic maps ⋮ On the stability of minimal submanifolds in conformal spheres ⋮ Explicit harmonic self-maps of complex projective spaces ⋮ Stable geodesic nets in convex hypersurfaces ⋮ Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds ⋮ Stability of exponentially harmonic maps ⋮ On the nonexistence of stable currents in submanifolds of a Euclidean space ⋮ On stable currents and positively curved hypersurfaces

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