Program
On the isoperimetric quotient over scalar-flat conformal classes
Student No.:20
Time:Friday 14:30-15:30, 2017.12.1
Instructor:熊金钢 Xiong Jingang  
Place:Conference Room 4, Floor 3, Jin Chun Yuan West Bldg.
Starting Date:2017-12-1
Ending Date:2017-12-1

Speaker: Prof. Jingang Xiong, Beijing Normal University [北京师范大学 熊金钢教授]
Title: On the isoperimetric quotient over scalar-flat conformal classes
Time: Friday 14:30-15:30, 2017/12/1
Place: 第四会议室Conference Room 4
Abstract: Let (M,g) be a smooth compact Riemannian manifold of dimension n with smooth boundary ∂M. Suppose that (M,g) admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric quotient over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality in the Euclidean space, and consequently is achieved, if either (i) n≥12 and ∂M has a nonumbilic point; or (ii) n≥10, ∂M is umbilic and the Weyl tensor does not vanish at some boundary point. This is joint with Tianling Jin.