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Dear all, <br class="">
<br class="">
This is Xiaodan Zhou from Analysis on metric spaces unit at Okinawa Institute of Science and Technology Graduate University. <br class="">
<br class="">
The next talk of our seminar is scheduled on <b class="">this coming Wednesday, August 11th 9 am. </b><br class="">
<br class="">
<b class="">Speaker</b>: Piotr Hajlasz, University of Pittsburgh<br class="">
<br class="">
<b class="">Title</b>: Lipschitz mappings, metric differentiability, and factorization through metric trees<br class="">
<br class="">
<b class="">Abstract</b>: Given a Lipschitz map $f$ from a cube into a metric space, we find several equivalent conditions for $f$ to have a Lipschitz factorization through a metric tree. As an application we prove a recent conjecture of David and Schul. The
techniques developed for the proof of the factorization result yield several other new and seemingly unrelated results. We prove that if $f$ is a Lipschitz mapping from an open set in $\mathbb{R}^n$ onto a metric space $X$, then the topological dimension of
$X$ equals $n$ if and only if $X$ has positive $n$-dimensional Hausdorff measure. We also prove an area formula for length-preserving maps between metric spaces, which gives, in particular, a new formula for integration on countably rectifiable sets in the
Heisenberg group. The talk is based on my recent joint paper with my graduate student Behnam Esmayli.
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You can obtain a zoom link through the following registration page:</div>
<div class=""><a href="https://oist.zoom.us/meeting/register/tJ0vd-ChrTMvHtSObiZm_tBf6cJA4i5DRf4G" class="">https://oist.zoom.us/meeting/register/tJ0vd-ChrTMvHtSObiZm_tBf6cJA4i5DRf4G</a><br class="">
<div class=""><br class="">
More information of the seminar can be found here:</div>
<div class="">https://groups.oist.jp/aoms/2021-summer-analysis-metric-spaces-seminar-0<br class="">
<br class="">
Please feel free to contact me if there are any questions. <br class="">
<br class="">
Best regards,<br class="">
Xiaodan Zhou<br class="">
-------------------------------<br class="">
<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="">
<a href="mailto:xiaodan.zhou@oist.jp" class="">xiaodan.zhou@oist.jp</a><br class="">
<br class="">
<a href="https://groups.oist.jp/aoms" class="">https://groups.oist.jp/aoms</a></div>
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