5 citations · 9 across the 3 of their papers we have counts for
8 papers · 1 filter
Mass under the Ricci flow
Xianzhe Dai, Li Ma
In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show t…
On the Stability of Kähler-Einstein Metrics
Xianzhe Dai, Xiaodong Wang, Guofang Wei
Using spin structure we prove that Kähler-Einstein metrics with nonpositive scalar curvature are stable (in the direction of changes in conformal structures) as the critical po…
On the Stability of Riemannian Manifold with Parallel Spinors
Xianzhe Dai, Xiaodong Wang, Guofang Wei
Inspired by the recent work of Physicists Hertog-Horowitz-Maeda, we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result say…
Eta Invariant and Conformal Cobordism
Xianzhe Dai
In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the defin…
An Index Theorem for Toeplitz Operators on Odd Dimensional Manifolds with Boundary
Xianzhe Dai, Weiping Zhang
We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singe…
Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operators
Xianzhe Dai, Weiping Zhang
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.