PUBLICATIONS MATHÉMATIQUES DE L'IHES

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Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Publications Mathématiques de l'IHÉS, Volume 133 (2021), pp. 327-366
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If U:[0,+∞[×M is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation

∂ t U+H(x,∂ x U)=0,
where M is a not necessarily compact manifold, and H is a Tonelli Hamiltonian, we prove the set Σ(U), of points in ]0,+∞[×M where U is not differentiable, is locally contractible. Moreover, we study the homotopy type of Σ(U). We also give an application to the singularities of the distance function to a closed subset of a complete Riemannian manifold.

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DOI: 10.1007/s10240-021-00125-5

Piermarco Cannarsa 1; Wei Cheng 1; Albert Fathi 1

1 
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     title = {Singularities of solutions of time dependent {Hamilton-Jacobi} equations. {Applications} to {Riemannian} geometry},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     year = {2021},
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     doi = {10.1007/s10240-021-00125-5},
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Piermarco Cannarsa; Wei Cheng; Albert Fathi. Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry. Publications Mathématiques de l'IHÉS, Volume 133 (2021), pp. 327-366. doi: 10.1007/s10240-021-00125-5

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