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The Weyl Problem With Nonnegative Gauss Curvature In Hyperbolic Space

Published online by Cambridge University Press:  20 November 2018

Jui-En Chang  and
Ling Xiao
Jui-En Chang
Affiliation:
Department of Mathematics, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218-2686, USA. e-mail: jchang@math.jhu.edu
Ling Xiao
Affiliation:
Department of Mathematics, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218-2686, USA. e-mail: lxiao@math.jhu.edu
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Abstract

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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.

Keywords

53A9935J1558J05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 1 , 01 February 2015 , pp. 107 - 131
Copyright
Copyright © Canadian Mathematical Society 2015

References

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