Curve shortening flow on Riemann surfaces with conical singularities (Q6624791)
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scientific article; zbMATH DE number 7932359
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Curve shortening flow on Riemann surfaces with conical singularities |
scientific article; zbMATH DE number 7932359 |
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Curve shortening flow on Riemann surfaces with conical singularities (English)
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28 October 2024
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The results in this article revolve around the question of curve shortening in the setting of Riemann surfaces that exhibit conformal conical singularities. The authors reduce this study to the investigation of degenerate quasilinear parabolic equations for which they discuss short time existence, uniqueness, and regularity of the flow. The approach implements the Gauss-Bonnet formula for singular surfaces with boundary, properties of sectorial operators and various tools in Mellin-Sobolev spaces.
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curve shortening flow
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Riemann surfaces
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conical singularities
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quasilinear parabolic equations
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