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The Weyl Problem With Nonnegative Gauss Curvature In Hyperbolic Space

  • Jui-En Chang,
    Department of Mathematics , Johns Hopkins University , 3400 North Charles Street , Baltimore, MD 21218-2686 , USA
  • Ling Xiao,
    Department of Mathematics , Johns Hopkins University , 3400 North Charles Street , Baltimore, MD 21218-2686 , USA
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Abstract

In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form $H$ and extend the result to $n$-dimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.
MSC Classifications: 53A99, 5J15, 58J05 show english descriptions None of the above, but in this section
unknown classification 5J15
Elliptic equations on manifolds, general theory [See also 35-XX]
53A99 - None of the above, but in this section
5J15 - unknown classification 5J15
58J05 - Elliptic equations on manifolds, general theory [See also 35-XX]
 

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