Published on:

7 February 2024

Primary Category:

Differential Geometry

Paper Authors:

Ronaldo F. de Lima,

Álvaro K. Ramos,

João Paulo dos Santos

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Proves existence of families of helicoidal rotator-translator solitons to MCF in H^2 x R

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Solitons rotate about axis and translate vertically under flow

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Generating curves trace out two infinite spiral arms in H^2

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Arms are properly embedded, centered at a point in H^2

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Flow translates surfaces vertically and rotates them about axis

Helicoidal surfaces flowing by mean curvature in H^2 x R

This paper establishes the existence of one-parameter families of helicoidal surfaces in the Riemannian product H^2 x R. These surfaces evolve under mean curvature flow by simultaneously rotating about a vertical axis and translating vertically. The generating curves trace out two infinite properly embedded spiral arms in H^2 centered at a point.

Classification of helicoidal surfaces by mean curvature

A general audience guide to helix surfaces in anti-de Sitter space

Solitons of surfaces evolving by mean curvature in the sphere cross the line

Families of genus 2 curves with real multiplication

Mean curvature flow of high codimension submanifolds in complex projective space

Simplified classification of hyperbolic space horo-shrinkers

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