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Heat Flow for Extrinsic Biharmonic Maps with Small Initial Energy

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Abstract

Let M m and N n↪ℝk be two compact Riemannian manifolds without boundary. We consider the L 2 gradient flow for the energy F(u):=\(\frac{1}{2}\)∫ M |Δu|2. If m≤ 3 or if m= 4 and F(u 0) is small, we show that the heat flow for extrinsic biharmonic maps exists for all time, and that the solution subconverges to a smooth extrinsic biharmonic map as time goes to infinity.

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  1. Mathematisches Institut der Universität Freiburg, Eckerstr 1, 79104, Freiburg, Germany

    Tobias Lamm

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  1. Tobias Lamm
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Lamm, T. Heat Flow for Extrinsic Biharmonic Maps with Small Initial Energy. Annals of Global Analysis and Geometry 26, 369–384 (2004). https://doi.org/10.1023/B:AGAG.0000047526.21237.04

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  • DOI: https://doi.org/10.1023/B:AGAG.0000047526.21237.04

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