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math.DG2026
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…
math.DG2025
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…
math.DG2025
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…