Type: Seminar

Distribution: World

Expiry: 6 Mar 2023

CalTitle1: On a class of GJMS equations on the standard n-sphere

Auth: sanjana@165.225.115.97 (sbha9594) in SMS-SAML

Dear friends and colleagues,
## Webinar Speaker

on **Monday, 6 March 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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Associate Professor **Quoc Anh Ngo ** is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

On a class of GJMS equations on the standard n-sphere

**Abstract:**

In a recent work by F. Hang and P. Yang (Int. Math. Res. Not. IMRN, 2020), a linear perturbation approach was used to tackle the sharp Sobolev inequality for the Paneitz operator on the standard 3-sphere S^3. This route leads to a class of linearly perturbed critical Paneitz equations of order 4 on S^3. From the geometric point of view, the nonlinearity of these fourth order equations contains a negative exponent which costs some analytical difficulty. As a result and supported by much evidence, it was conjectured by them if positive smooth solutions to these fourth order equations are nothing but constant if the perturbation is sufficiently small in an appropriate sense. In this talk, based on joint work with Ali Hyder, I will introduce new ingredients to tackle the above conjecture in a more general framework. More precisely, we are interested in linearly perturbed critical/subcritical GJMS equations of order 2m on S^n with n<2m. The main finding indicates that if the perturbation is sufficiently small, then any positive smooth solution to these higher-order equations must be constant. In particular, this provides an affirmative answer to the conjecture. Comments on the case n>2m are also made if time permits.

**Chair:** Yoshikazu Giga (Professor @ Tokyo 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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Quoc Anh Ngo

Associate Professor @ Vietnam National University, Hanoi

Mr. Quoc Anh Ngo obtained his Ph.D. from the National University of Singapore in 2013, under the supervision of Professor Xingwang Xu. After graduation, he held a postdoctoral position at the Université de Tours and a research fellowship at the National University of Singapore. He was also an ICTP Associate at the International Centre for Theoretical Physics from 2015 to 2020. Between 2019 and 2020, he was appointed Project Researcher position at The University of Tokyo. The research interest of Mr. Ngo includes geometric analysis and partial differential equations with applications to mathematical physics and applied sciences. His contributions in these fields have been recognized by the Tosio Kato Fellowship awarded in 2018. He is currently an associate professor at Vietnam National University in Hanoi.

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