**SMS scnews item created by Haotian Wu at Fri 24 Mar 2017 1841**

Type: Seminar

Modified: Sat 25 Mar 2017 1006

Distribution: World

Expiry: 23 Sep 2017

**Calendar1: 30 Mar 2017 1000-1100**

**CalLoc1: Carslaw 535A**

CalTitle1: Geometry & Topology Seminar: Hung Tran -- Index of A Free Boundary Minimal Surface

Auth: haotianw@como.maths.usyd.edu.au

### Geometry & Topology Seminar

# Index of A Free Boundary Minimal Surface

### Hung Tran (UC Irvine)

**Thursday 30 March 10:00–11:00 in Carslaw 535A.**

Please join us for lunch after 13:00!

**Abstract:**
A FBMS in the unit Euclidean ball is a critical point of the area functional among all surfaces with boundaries in the unit sphere, the boundary of the ball. The Morse index gives the number of distinct admissible deformations which decrease the area to second order. In this talk, we explain how to compute the index from data of two simpler problems. The ﬁrst one is the corresponding problem with ﬁxed boundary condition; the second is associated with the Dirichlet-to-Neumann map for Jacobi ﬁelds. We also discuss applications to a conjecture about FBMS with index 4 in comparison with the Willmore conjecture.