$C^{1,\alpha}$ isometric extensions

L\'aszl\'o Sz\'ekelyhidi Jr; Wentao Cao

arxiv: 1806.07335 · v1 · pith:AM5OPC4Ynew · submitted 2018-06-19 · 🧮 math.DG · math.AP

C^(1,α) isometric extensions

Wentao Cao , L\'aszl\'o Sz\'ekelyhidi Jr This is my paper

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keywords isometricalphaextensionscauchycodimensionconsiderconstructconvex

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In this paper we consider the Cauchy problem for isometric immersions. More precisely, given a smooth isometric immersion of a codimension one submanifold we construct $C^{1,\alpha}$ isometric extensions for any $\alpha<\frac{1}{n(n+1)+1}$ via the method of convex integration.

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C^(1,α) isometric extensions

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