3 papers
math.DG2026
Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds
Pengshuai Shi
On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schrödinger operators. Assuming two Dirac…
math.DG2025
The odd-dimensional long neck problem via spectral flow
Pengshuai Shi
In this paper, we establish a scalar-mean curvature comparison theorem for the long neck problem on odd-dimensional spin manifolds. This extends previous work of Cecchini and Zeidl…
math.DG2025
Spectral flow of Callias operators, odd K-cowaist, and positive scalar curvature
Pengshuai Shi
On a complete Riemannian manifold , we study the spectral flow of a family of Callias operators. We derive a codimension zero formula when the dimension of is odd and a codi…