Curve shortening flow on Riemann surfaces with conical singularities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914607440855040 |
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| author | Roidos, Nikolaos Savas-Halilaj, Andreas |
| author_facet | Roidos, Nikolaos Savas-Halilaj, Andreas |
| contents | We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evolution is governed by a degenerate quasilinear parabolic equation. In this case, we establish short time existence, uniqueness, and regularity of the flow. We also show that the evolving curves stay fixed at the singular points of the surface and obtain some collapsing and convergence results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_01024 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Curve shortening flow on Riemann surfaces with conical singularities Roidos, Nikolaos Savas-Halilaj, Andreas Differential Geometry Analysis of PDEs Functional Analysis We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through the singular points, then the evolution is governed by a degenerate quasilinear parabolic equation. In this case, we establish short time existence, uniqueness, and regularity of the flow. We also show that the evolving curves stay fixed at the singular points of the surface and obtain some collapsing and convergence results. |
| title | Curve shortening flow on Riemann surfaces with conical singularities |
| topic | Differential Geometry Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2007.01024 |