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Spacelike hypersurfaces with prescribed boundary values and mean curvature

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Abstract

We consider the boundary-value problem for the mean curvature operator in Minkowski space, and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions. Our main results hold for non-constant mean curvature, and make no assumptions about the smoothness of the boundary or boundary data.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Robert Bartnik

  2. Department of Mathematics, Australian National University, 2600, Canberra, A.C.T., Australia

    Leon Simon

Authors
  1. Robert Bartnik
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  2. Leon Simon
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Communicated by S.-T. Yau

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Bartnik, R., Simon, L. Spacelike hypersurfaces with prescribed boundary values and mean curvature. Commun.Math. Phys. 87, 131–152 (1982). https://doi.org/10.1007/BF01211061

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  • DOI: https://doi.org/10.1007/BF01211061

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