Abstract
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.
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Christoforou, C., Slemrod, M. Isometric immersions via compensated compactness for slowly decaying negative Gauss curvature and rough data. Z. Angew. Math. Phys. 66, 3109–3122 (2015). https://doi.org/10.1007/s00033-015-0591-1
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DOI: https://doi.org/10.1007/s00033-015-0591-1