boundary conditions 1counterexample 1dirac operators 1gromov conjecture 1index theory 1manifolds with corners 1
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math.DG2026
Remarks on the paper "On Gromov's dihedral extremality and rigidity conjectures" by Jinmin Wang, Zhizhang Xie and Guoliang Yu
Christian Baer, Bernhard Hanke, Thomas Schick
The authors present a counterexample to an index calculation used in a recent paper on self‑adjoint extensions of Dirac‑type operators on manifolds with corners, showing that the c…
math.DG2024
Boundary conditions for scalar curvature
Christian Baer, Bernhard Hanke
Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area.…
math.DG2024
Scalar curvature rigidity of warped product metrics
Christian Baer, Simon Brendle, Bernhard Hanke +1
We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This…