Curve shortening flow on Riemann surfaces with conical singularities
type: Item
instance of: scholarly article
title: Curve shortening flow on Riemann surfaces with conical singularities
author: Nikolaos Roidos
author: Andreas Savas-Halilaj
published in: Mathematische Annalen
publication date: 2024-10-28T00:00:00Z
review text: 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.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 53E10
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K93
Mathematics Subject Classification ID: 35R01
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47B12
zbMATH DE Number: 7932359
zbMATH Keywords: curve shortening flow
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: conical singularities
zbMATH Keywords: quasilinear parabolic equations
MaRDI profile type: Publication
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Curve shortening flow on Riemann surfaces with conical singularities (DOI)
DOI: 10.1007/S00208-024-02813-Z