[geometry-ml:04418] OIST Analysis on metric spaces seminar this week

[Xiaodan Zhou]

Dear all,

This is Xiaodan Zhou from Analysis on metric spaces unit at Okinawa Institute of Science and Technology Graduate University.

The next talk of our seminar is scheduled on this coming Friday, August 27th 9 am.

Speaker: Luca Capogna, Smith College

Title: Curve shrinking flow in Carnot Groups

Abstract: This is a preliminary report on a joint project with Enrico Le Donne (University of Fribourg, Switzerland). Motivated by the study of geodesics in sub-Riemannian geometry, we use techniques from Lie group geometry and Calculus of Variations to derive a system of PDE that describes the gradient flow of the length functional for horizontal (i.e. tangent to the first layer of the Lie algebra stratification) curves in a rank-two Carnot group of arbitrary step. Similarly to the Euclidean area-preserving curve shrinking flow, our PDE has a nonlocal term, which arises in view of the non- holonomic constraint, i.e. for each time the curve must be horizontal. We prove short time existence for the flow, if the initial data is a non-abnormal horizontal curve, and provide some indications of what happens in the abnormal case.

You can obtain a zoom link through the following registration page:
https://oist.zoom.us/meeting/register/tJIqcOGorz8tEtbK7mfo8mw_kbcD2uac5B_r

More information of the seminar can be found here:
https://groups.oist.jp/aoms/2021-summer-analysis-metric-spaces-seminar-0

Please feel free to contact me if there are any questions.

Best regards,
Xiaodan Zhou
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Analysis on Metric Spaces Unit
Okinawa Institute of Science and Technology Graduate University
Okinawa 904-0495, Japan
xiaodan.zhou ＠ oist.jp

https://groups.oist.jp/aoms




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