Scientific Calendar Event

Starts 22 Nov 2023 15:00
Ends 22 Nov 2023 17:00
Central European Time
IGAP/IFPU Building
IGAP/IFPU Building-room 205
Via Beirut 2 - 34151 Trieste
Abstract: We aim to introduce a structural strategy to produce new minimal submanifolds in spheres based on two given ones. The method is to spin a pair of given minimal submanifolds by a curve $\gamma\subset\mathbb S^3$ in a balanced way and leads to resulting minimal submanifolds -- spiral minimal products, which form a two-dimensional family arising from intriguing pendulum phenomena decided by $C$ and $\tilde C$. With $C=0$, we generalize the construction of minimal tori in $\mathbb S^3$ explained in a paper by Brendle to higher dimensional situations. When $C=-1$, we recapture previous relative work by Castro-Li-Urbano and Haskins-Kapouleas for special Legendrian submanifolds in spheres, and moreover, can gain numerous $\mathscrC$-totally real and totally real embedded minimal submanifolds in spheres and in complex projective spaces respectively. A key ingredient of the paper is to apply the beautiful extension result of minimal submanifolds by Harvey-Lawson for a rotational reflection principle in our situation to establish $\gamma$. The talk is based on a joint work with Prof. Haizhong Li.