Research profile

Luis Vega

Works on other curvature flows.

NP-RC-9115750000-0001-5086-6345

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Other curvature flows

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  1. Valeria Banica

    1 joint worklatest 2020

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2020

math.APWider flowsarXiv:2007.07184

Riemann's non-differentiable function and the binormal curvature flow

Valeria Banica, Luis Vega

We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious nonlinear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.

Other curvature flows
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NP-RC-911575 is Luis Vega'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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