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A Note on $p$-Harmonic $1$-Forms on Complete Manifolds

  Published:2001-09-01
 Printed: Sep 2001
  • Xi Zhang
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Abstract

In this paper we prove that there is no nontrivial $L^{q}$-integrably $p$-harmonic $1$-form on a complete manifold with nonnegatively Ricci curvature $(0
Keywords: $p$-harmonic, $1$-form, complete manifold, Sobolev inequality $p$-harmonic, $1$-form, complete manifold, Sobolev inequality
MSC Classifications: 58E20, 53C21 show english descriptions Harmonic maps [See also 53C43], etc.
Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
58E20 - Harmonic maps [See also 53C43], etc.
53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
 

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