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Showing 2012 · math.DGShow all
3 papers · 2 filters
math.DG2012★ 2 cited
The Weyl problem with nonnegative Gauss curvature in hyperbolic space
Jui-En Chang, Ling Xiao
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…
math.DG2012★ 2 cited
Ricci curvature and monotonicity for harmonic functions
Tobias Holck Colding, William P. Minicozzi
In this paper we generalize the monotonicity formulas of [C] for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g.…
math.DG2012★ 4 cited
On uniqueness of tangent cones for Einstein manifolds
Tobias Holck Colding, William P. Minicozzi
We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any nonc…