Eigenvalue Estimates and Geometric Rigidity of Hypersurfaces

Add to your list(s) Download to your calendar using vCal

• Abhitosh Upadhyay (Indian Institute of Technology)
• Thursday 05 February 2026, 16:35-16:50
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

In this talk, I will begin with a brief review of some foundational geometric inequalities for hypersurfaces in Euclidean spaces focusing on those where equality charaacterizes the standared geodesic spheres. A prime example is Reilly’s celebraated inequality which provides a sharp upper bound for the first non trivial eigenvalue of the Laplace Beltrami-operator on compact, embedded hypersurfaces. Interestingly, these inequalities can often be traced back to a fundamental estimate involving the $L^{2$ norm of the position vector. I will then delve into a novel stability refinement of this inequality: we establish that if a hypersurface nearly attains this lower bound on the $L}2$-norm, then it must be geometrically close, in a suitable sense, to a round sphere.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31
• dh539

Note that ex-directory lists are not shown.