Rigidity and vanishing theorems for complete translating solitons

Thời gian: 9h00 (Giờ VN), thứ năm, ngày 06/04/2023.

Online: (google meet) https://meet.google.com/yyb-zhod-hdy?authuser=3&hl=vi

Tóm tắt: In this talk, I will introduce some rigidity theorems for complete translating solitons. Assume that the $L^q$-norm of the trace-free second fundamental form is finite, for some $qinmathbb{R}$ and using a Sobolev inequality, we show that translators must be hyperspaces. Moreover, we also investigate a vanishing property for translators which states that there are no nontrivial $L_f^p (pgeq2)$ weighted harmonic $1$-forms on ${M}$ if the $L^n$-norm of the second fundamental form is bounded. This talk is based on a joint work with H.T. Dung and T.Q. Huy.