<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">幾何学MLの皆様<br class=""><br class="">福岡大学の柳青と申します．下記の要領でセミナーを開催いたします．<br class="">皆様のご参加をお待ちしております．<br class=""><br class="">日時：2019年7月29日(月) 15:00--16:50<br class="">場所：福岡大学９号館４階大学院講義室３（9444室）<br class=""><br class="">15:00--15:50<br class="">講演者：Nageswari Shanmugalingam氏（University of Cincinnati）<br class="">題目：Characterization of quasiconformal mappings in terms of modulus of families of sets of finite perimeter<br class=""><br class="">要旨：A metric measure space is said to be of Q-bounded geometry for some Q>1 if the measure on the space is Ahlfors Q-regular and supports a Q-Poincar\'e inequality. From the work of Heinonen and Koskela, it is well-known that a homeomorphism between two such spaces is quasiconformal if and only if that homeomorphism quasi-preserves the Q-modulus of families of paths in the space. In this talk we will discuss a related characterization of quasiconformal mappings in terms of quasi-preservation of the Q/(Q-1)-modulus of families of bounded sets of finite perimeter.<br class=""><br class=""><br class="">16:00--16:50<br class="">講演者：Xiaodan Zhou氏（Worcester Polytechnic Institute）<br class="">題目：Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations<br class=""><br class="">要旨：This talk introduces a notion of horizontal convex envelopes of continuous functions in the Heisenberg group. We provide a convexification operator to find the envelope in a constructive manner. We also apply the convexification process to show h-convexity of viscosity solutions to a class of fully nonlinear elliptic equations in the Heisenberg group satisfying a certain symmetry condition. Our examples show that in general one cannot expect h-convexity of solutions without the symmetry condition. <br class=""><br class="">-------------------------<br class="">セミナー終了後，18時より懇親会を予定しております．<br class="">ご参加頂ける方は，7月25日(木)までに柳（<a href="mailto:qingliu@fukuoka-u.ac.jp" class="">qingliu@fukuoka-u.ac.jp</a>）<br class="">までご連絡いただけますと幸いです．<br class=""><br class="">柳青<br class="">福岡大学理学部応用数学科<br class=""><div class=""><br class=""></div><div class=""><br class=""></div></body></html>