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On Donaldson’s flow of surfaces in a hyperkähler four-manifold

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Abstract

We prove some basic properties of Donaldson’s flow of surfaces in a hyperkähler 4-manifold. When the initial submanifold is symplectic with respect to one Kähler form and Lagrangian with respect to another, we show that certain kinds of singularities cannot form, and we prove a convergence result under a condition related to one considered by M.-T. Wang for the mean curvature flow.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Jian Song

  2. Department of Mathematics, Imperial College, London, SW7 2AZ, UK

    Ben Weinkove

Authors
  1. Jian Song
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  2. Ben Weinkove
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Correspondence to Jian Song.

Additional information

The second author is supported in part by National Science Foundation grant DMS-05-04285, and is currently on leave from Harvard University, supported by a Royal Society Research Assistantship.

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Song, J., Weinkove, B. On Donaldson’s flow of surfaces in a hyperkähler four-manifold. Math. Z. 256, 769–787 (2007). https://doi.org/10.1007/s00209-007-0102-y

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  • DOI: https://doi.org/10.1007/s00209-007-0102-y

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