7 papers · 1 filter
Sharp parameter gaps for quantized Mabuchi energies and cscK metrics
Kefeng Liu, Liangdi Zhang
For polarized manifolds, we show that semistability for the quantized Mabuchi energy at one fixed finite parameter is equivalent to uniform K-stability and to unique existence of c…
Higgs-Demailly System and Positivity of Higgs Bundles
Liangdi Zhang
We prove that the Higgs--Demailly system on a compact Riemann surface admits, for suitable fixed parameters, a smooth admissible solution at its terminal parameter if and only if t…
Existence and geometry of Hermitian metrics with constant second scalar curvature
Liangdi Zhang
We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature within balance…
First eigenvalue estimates on complete balanced Hermitian manifolds
Liangdi Zhang
We establish lower bounds for the first positive eigenvalue of the Laplace--de Rham operator on complete balanced Hermitian manifolds in terms of curvature of the Strominger--Bismu…
Kählerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures
Liangdi Zhang
We prove several Kählerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key too…
New curvature characterizations for spherical space forms and complex projective spaces
Xiaokui Yang, Liangdi Zhang
In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space $\…
Existence of the -Ricci-Yamabe flow on closed manifolds
Liangdi Zhang
On a smooth closed Riemannian manifold, we show short time existence of smooth solutions to the -Ricci-Yamabe flow, which is a natural generalization of the Ricci flow and t…