5 papers · 1 filter
Stable systolic inequalities via mod n covering
Aditya Kumar
We introduce a mod covering based approach to stable systolic inequalities. The idea is to prescribe a cohomology class mod which forces the desired cup product or index to…
Urysohn width and macroscopic scalar curvature
Aditya Kumar, Balarka Sen
We show that the macroscopic version of Gromov's Urysohn width conjecture for scalar curvature is false in dimensions four and above. This is based on (1) a novel estimate on the c…
Positive scalar curvature and exotic structures on simply connected four manifolds
Aditya Kumar, Balarka Sen
We address Gromov's band width inequality and Rosenberg's -stability conjecture for simply connected smooth four manifolds. Both results are known to be false in dimension 4 d…
Circle bundles with PSC over large manifolds
Aditya Kumar, Balarka Sen
We construct infinitely many examples of macroscopically large manifolds of dimension equipped with circle bundles whose total spaces admit metrics of positive scalar cu…
The first Steklov eigenvalue on manifolds with nonnegative Ricci curvature and convex boundary
Jonah A. J. Duncan, Aditya Kumar
We establish a new lower bound for the first non-zero Steklov eigenvalue of a compact Riemannian manifold with non-negative Ricci curvature and (strictly) convex boundary. Related…