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Euclidean Complete Hypersurfaces with Negative Constant Affine Mean Curvature

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Abstract.

Given a constant L 1 < 0 and a bounded convex domain \(\Omega \subset {\mathbb{R}}^{n}\) with prescribed boundary value data in terms of a smooth strictly convex function φ, we construct an Euclidean complete hypersurface with constant affine mean curvature L 1.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, 610064, Chengdu, Sichuan Prov., P.R. China

    Baofu Wang & An-Min Li

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  1. Baofu Wang
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  2. An-Min Li
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Correspondence to Baofu Wang.

Additional information

Dedicated to Udo Simon on the occasion of his 70th birthday

The first author is partially supported by NSFC 10771146 and RFDP. The second author is partially supported by NKBRPC(2006CB805905), NSFC 10631050 and RFDP.

Submitted: September 20, 2007. Received: March 12, 2008. Revised: March 14, 2008.

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Wang, B., Li, AM. Euclidean Complete Hypersurfaces with Negative Constant Affine Mean Curvature. Result. Math. 52, 383–398 (2008). https://doi.org/10.1007/s00025-008-0320-6

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  • DOI: https://doi.org/10.1007/s00025-008-0320-6

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