Type: Seminar

Modified: Thu 9 Feb 2023 1049

Distribution: World

Expiry: 13 Feb 2023

Auth: sanjana@149.167.172.52 (sbha9594) in SMS-SAML

Dear friends and colleagues,
## Webinar Speaker

on **Monday, 13 February 2023** at

•**12:00 PM** for Beijing, Hong Kong and Perth

•**01:00 PM** for Seoul and Tokyo

•**03:00 PM** for Canberra, Melbourne and Sydney

•**05:00 PM** for Auckland

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Research Fellow ** Dr Kwok-Kun Kwong** is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Effect of the average scalar curvature on Riemannian manifolds

**Abstract:**

The well-known Bishop-Gromov volume comparison theorem says that if the Ricci curvature is bounded below by (n-1)k, then the volumeof a metric ball is at most that of the volume of the ball with the same
radius in the space form with curvature k. Counterexamples show that the Ricci curvature cannot be replaced by the scalar curvature in the assumption. On the other hand, a Taylor series computation shows that the scalar curvature does tend to decrease the volume of small geodesic balls. In this talk, I will illustrate how the average scalar curvature (together with the Ricci curvature) of a closed manifold affects the average volume of its metric balls of any size. This gives an improvement of the Bishop-Gromov estimate. I will also show its effect on the average total mean curvature of geodesic spheres of radius up to the injectivity radius.

**Chair:** Ben Andrews (Professor@ Australian National University)

More information and how to attend this talk can be found at the seminar webpage

Sanjana

On behalf of Daniel H. and Ben

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Kwok-Kun Kwong

Reseach Fellow @ the Australian National University in Canberra

Kwok-Kun obtained his PhD from The Chinese University of Hong Kong in 2011, under the supervision of Professor Luen-Fai Tam. His research interests include differential geometry, Riemannian and Lorentzian geometry, and mathematical relativity. He is currently a Research Fellow at Australian National University. Before coming to ANU, he has worked at University of Miami, National Cheng Kung University, University of Sydney and University of Wollongong.

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