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

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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Key Details

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

Solitons rotate about axis and translate vertically under flow

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

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

Flow translates surfaces vertically and rotates them about axis

AI generated summary

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.

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