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"On the genus and area of constant mean curvature surfaces with bounded index"

Geometry-Topology Seminar

Thursday, November 5, 2020 - 4:30pm

Artur Bicalho Saturnino

UPenn

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/91890239234 This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

Using the local picture of the degeneration of sequences of minimal surfaces developed by Chodosh, Ketover and Maximo we show that in any closed Riemannian 3-manifold (M,g), the genus of an embedded CMC surface can be bounded only in terms of its index and area, independently of the value of its mean curvature. We also show that if M has finite fundamental group, the genus and area of any non-minimal embedded CMC surface can be bounded in terms of its index and a lower bound for its mean curvature.