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Geroch monotonicity and the construction of weak solutions of the inverse mean curvature flow


Reference:

Moser, R., 2014. Forthcoming. Geroch monotonicity and the construction of weak solutions of the inverse mean curvature flow. Asian Journal of Mathematics

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    Abstract

    For surfaces evolving under the inverse mean curvature flow, Geroch observed that the Hawking mass is a Lyapunov function. For weak solutions of the flow, the corresponding monotonicity formula was proved by Huisken and Ilmanen. An analogous formula exists for approximate equations as well, and it provides uniform control of the solutions in certain Sobolev spaces. This helps to construct weak solutions under very weak assumptions on the initial data.

    Details

    Item Type Articles
    CreatorsMoser, R.
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusIn Press
    ID Code23335

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