https://neckpinch.com/authors/nikolaos-roidos/New arXiv papers by Nikolaos Roidos, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2007.01024/arxiv:2007.01024Thu, 02 Jul 2020 00:00:00 GMTNikolaos Roidos, Andreas Savas-Halilaj — 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.Curve shorteningSingularities(Non)collapsingSurfacesStability & uniquenessHarmonic maps & DeTurck trick https://neckpinch.com/papers/1807.04139/arxiv:1807.04139Wed, 11 Jul 2018 00:00:00 GMTNikolaos Roidos — We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we show well posedness of the short time solution in the L^q-setting. Moreover, we give a picture of the deformation of the conical tips under the flow by providing an asymptotic expansion of the evolving metric close to the boundary in terms of the initial local geometry. Due to the blow up of the scalar curvature close to the singularities we use maximal L^q-regularity theory for conically degenerate operators.Yamabe flowSingularitiesScalar curvature