240 citations · 267 across the 9 of their papers we have counts for
10 papers
Dirac eigenvalues and the hyper-hemispherical radius
Pengshuai Shi
On a connected compact Riemannian spin manifold with boundary, we prove an upper estimate for the smallest eigenvalue of the Dirac operator under the boundary condition associated…
The relative eta invariant for a pair of Dirac-type operators on non-compact manifolds
Pengshuai Shi
Let and be two self-adjoint Fredholm Dirac-type operators defined on two non-compact manifolds. If they coincide at infinity so that the relative he…
REBOUNDx: A Library for Adding Conservative and Dissipative Forces to Otherwise Symplectic N-body Integrations
Daniel Tamayo, Hanno Rein, Pengshuai Shi +1
Symplectic methods, in particular the Wisdom-Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophys…
The index of a local boundary value problem for strongly Callias-type operators
Maxim Braverman, Pengshuai Shi
We consider a complete Riemannian manifold M whose boundary is a disjoint union of finitely many complete connected Riemannian manifolds. We compute the index of a local boundary v…
Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds
Pengshuai Shi
We study the Cauchy data spaces of the strongly Callias-type operators using maximal domain on manifolds with non-compact boundary, with the aim of understanding the Atiyah-Patodi-…
APS index theorem for even-dimensional manifolds with non-compact boundary
Maxim Braverman, Pengshuai Shi
We study the index of the APS boundary value problem for a strongly Callias-type operator on a complete even dimensional Riemannian manifold (the odd dimensional case was c…
The Atiyah-Patodi-Singer index on manifolds with non-compact boundary
Maxim Braverman, Pengshuai Shi
We study the index of the APS boundary value problem for a strongly Callias-type operator D on a complete Riemannian manifold . We show that this index is equal to an index on a…
The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions
Pengshuai Shi
We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact…
Cobordism Invariance of the Index of Callias-Type Operators
Maxim Braverman, Pengshuai Shi
We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prov…
Singularities of Connection Ricci Flow and Ricci Harmonic Flow
Pengshuai Shi
In this paper, we study the singularities of two extended Ricci flow systems --- connection Ricci flow and Ricci harmonic flow using newly-defined curvature quantities. Specificall…