Location: ** Hill 705**

Date & time: Tuesday, 06 March 2018 at 1:40PM - 2:40PM

** **

Abstract: A classical result of Heinz states that, if a convex graph in \(R^3\) with positive smooth Gauss curvature, then there is an interior \(C^2\) estimate. The problem is reduced to \(2\)-dimensional Monge-Ampere equation. Such interior estimate is false for Monge-Ampere equation when dimension is larger than or equal to \(3\), by Pogorelov's example. The work of Urbas also indicates the failure of interior estimate for \(\sigma_k\) curvature and Hessian equations when \(k>2\). A longstand problem is where interior estimate is true for \(k=2\) in general dimensions. In the talk, we provide an affirmative answer for all convex solutions. In case of isometrically immersed hypersurfaces in \(R^{n+1}\) with positive scalar curvature, convexity assumption can be dropped. These estimates are consequences of an interior estimates for these equations obtained under a weakened condition.

This is a joint work with Guohuan Qiu.

Arthur Wang Organizer's Page

Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang, Rick Falk Organizer's Page

Xiaojun Huang, Jian Song, Sagun Chanillo

Pranjal Awasthi, Shubhangi Saraf Organizer's Page

Jeffry Kahn, Bhargav Narayanan, Abigail Raz Organizer's Page

Bryan Ek, Doron Zeilbrger Organizer's Page

Paul Feehan, Manousos Maridakis, Natasa Sesum seminar webpage

Borisov, Diaconescu, Tarasca, Woodward

Alejandro Ginory Organizer's Page

Jason Saied, Corrine Yap Organizer's Page

Erik De Amorim Organizer's Page

Yonah Biers-Ariel Organizer's Page

Katie McKeon Organizer's Page

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's page

Grigor Sargsyan seminar website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis

Matthew C Welsh

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Claire Burrin seminar website

Stephen D. Miller

Matthew Charnley Organizer's Page

Feng Luo, Xiaochun Rong, Hongbin Sun Organizer's page

M. Lienert seminar webpage

Organizer: Vladimir Retakh Organizer's page

Claire Burrin, Amita Malik, Kei Nakamura

- Show events from all categories

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

*Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.*

Department of Mathematics
Rutgers University Hill Center - Busch Campus 110 Frelinghuysen Road Piscataway, NJ 08854-8019, USA Phone: +1.848.445.2390 Fax: +1.732.445.5530 |