Research profile

Nikolaos Roidos

Works on Yamabe flow, harmonic maps & DeTurck trick and curve shortening.

NP-RC-9491020000-0002-9291-0903

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Yamabe flowHarmonic maps & DeTurck trickCurve shorteningSingularitiesSurfaces(Non)collapsingScalar curvatureStability & uniqueness

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  1. Andreas Savas-Halilaj

    1 joint worklatest 2020

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2020

math.DGWider flowsv3arXiv:2007.01024

Curve shortening flow on Riemann surfaces with conical singularities

Nikolaos 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
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2018

math.APWider flowsv2arXiv:1807.04139

Conic manifolds under the Yamabe flow

Nikolaos 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 -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 -regularity theory for conically degenerate operators.

Yamabe flowSingularitiesScalar curvature
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NP-RC-949102 is Nikolaos Roidos's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

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