[geometry-ml:03776] セミナーのご案内

[Qing Liu]

幾何学MLの皆様

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．
皆様のご参加をお待ちしております．

日時：2019年7月29日(月) 15:00--16:50
場所：福岡大学９号館４階大学院講義室３（9444室）

15:00--15:50
講演者：Nageswari Shanmugalingam氏（University of Cincinnati）
題目：Characterization of quasiconformal mappings in terms of modulus of families of sets of finite perimeter

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.


16:00--16:50
講演者：Xiaodan Zhou氏（Worcester Polytechnic Institute）
題目：Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations

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. 

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セミナー終了後，18時より懇親会を予定しております．
ご参加頂ける方は，7月25日(木)までに柳（qingliu ＠ fukuoka-u.ac.jp <mailto:qingliu ＠ fukuoka-u.ac.jp>）
までご連絡いただけますと幸いです．

柳青
福岡大学理学部応用数学科



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