4 papers · 1 filter
The continuity equation on Hopf and Inoue surfaces
Xi Sisi Shen, Kevin Smith
We study the continuity equation of La Nave-Tian, extended to the Hermitian setting by Sherman-Weinkove, on Hopf and Inoue surfaces. We prove a priori estimates for solutions in bo…
The Kähler-Ricci flow, holomorphic vector fields and Fano bundles
Xi Sisi Shen
We study the behavior of the Kähler-Ricci flow on compact manifolds developing finite-time singularities, in particular, when the flow contracts exceptional divisors or collapses t…
Estimates for metrics of constant Chern scalar curvature
Xi Sisi Shen
We prove a priori estimates for constant Chern scalar curvature metrics on a compact complex manifold conditional on an upper bound on the entropy, extending a recent result by Che…
On Parallel Transport in Wasserstein Space
Xi Sisi Shen
In this short note, we would like to give a construction of parallel transport for tangent cones lying in the interior of a geodesic in Wasserstein space. We give a complete proof…