Ilmanen, T;
Neves, A;
Schulze, F;
(2019)
ON SHORT TIME EXISTENCE FOR THE PLANAR NETWORK FLOW.
Journal of Differential Geometry
, 111
(1)
pp. 39-89.
10.4310/jdg/1547607687.
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Abstract
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White’s local regularity theorem for mean curvature flow. We also show a pseudolocality theorem for mean curvature flow in any codimension, assuming only that the initial submanifold can be locally written as a graph with sufficiently small Lipschitz constant.
| Type: | Article |
|---|---|
| Title: | ON SHORT TIME EXISTENCE FOR THE PLANAR NETWORK FLOW |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4310/jdg/1547607687 |
| Publisher version: | https://doi.org/10.4310/jdg/1547607687 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10064621 |
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