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# The Weyl Problem With Nonnegative Gauss Curvature In Hyperbolic Space

Published:2014-02-07
Printed: Feb 2015
• 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 - None of the above, but in this section 5J15 - unknown classification 5J1558J05 - Elliptic equations on manifolds, general theory [See also 35-XX]

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