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<div>Dear all, <br class="">
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This is Xiaodan Zhou from Analysis on metric spaces unit at Okinawa Institute of Science and Technology Graduate University. <br class="">
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The next talk of our seminar is scheduled on this coming <b class="">Friday, August 27th 9 am.</b> <br class="">
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<b class="">Speaker</b>: Luca Capogna, Smith College<br class="">
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<b class="">Title</b>: Curve shrinking flow in Carnot Groups
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<b class="">Abstract:</b> 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. <br class="">
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You can obtain a zoom link through the following registration page:<br class="">
<a href="https://oist.zoom.us/meeting/register/tJIqcOGorz8tEtbK7mfo8mw_kbcD2uac5B_r" class="">https://oist.zoom.us/meeting/register/tJIqcOGorz8tEtbK7mfo8mw_kbcD2uac5B_r</a></div>
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More information of the seminar can be found here:<br class="">
<a href="https://groups.oist.jp/aoms/2021-summer-analysis-metric-spaces-seminar-0" class="">https://groups.oist.jp/aoms/2021-summer-analysis-metric-spaces-seminar-0</a><br class="">
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Please feel free to contact me if there are any questions. <br class="">
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Best regards,<br class="">
Xiaodan Zhou<br class="">
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<br class="">
Analysis on Metric Spaces Unit<br class="">
Okinawa Institute of Science and Technology Graduate University<br class="">
Okinawa 904-0495, Japan<br class="">
xiaodan.zhou@oist.jp<br class="">
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https://groups.oist.jp/aoms</div>
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