Isometric immersions via compensated compactness for slowly decaying negative Gauss curvature and rough data
Date
2015Source
Zeitschrift fur Angewandte Mathematik und PhysikVolume
66Issue
6Pages
3109-3122Google Scholar check
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In this paper, the method of compensated compactness is applied to the problem of isometric immersion of a two-dimensional Riemannian manifold with negative Gauss curvature into three-dimensional Euclidean space. Previous applications of the method to this problem have required decay of order t−4 in the Gauss curvature. Here, we show that the decay of Hong (Commun Anal Geom 1:487−514, 1993) t−2−δ/2 where δ ∈ (0, 4) suffices. © 2015, Springer Basel.