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The heat flow for subharmonic orbits

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Abstract

LetV: M → ℝ be a smooth (potential) function on a compact Riemannian manifold. This gives rise to a second order Hamiltonian system. Assuming that the corresponding action functional is a Morse function, we will prove that the heat flow for subharmonics exists globally and converges to a critical point of the energy. As a Corollary, this shows the convergence of the geodesic heat flow (to a geodesic) without any curvature assumptions onM.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, CA, USA

    Benjamin G. Lorica

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  1. Benjamin G. Lorica
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Lorica, B.G. The heat flow for subharmonic orbits. Ann Glob Anal Geom 12, 9–17 (1994). https://doi.org/10.1007/BF02108285

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  • DOI: https://doi.org/10.1007/BF02108285

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