Speaker: 毕宇晨(中科院数学所)

Time： Dec 27, 15:00-17:00

Place： #腾讯会议：156-912-827 会议密码：无

Title：Bi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition（III）

Abstract: In this talk, we first review recent work of Lytchak and Wenger on harmonic maps with metric space target, paying more attention to conformality and homeomorphism. Then we apply their results to obtain a conformal parameterization for a chord-arc $2$-varifold. By invoking an old idea of Heinonen and Koskela, we show the conformal factor of this conformal parameterization is a Muckenhoupt $A_2$-weight. Finally, we finish the proof of the critical Allard regularity theorem with the help of the celebrated Coifman-Lions-Meyer-Semmes estimate. This is a joint work with Jie Zhou.