4 papers · 1 filter
Cone Conditions for the Curvature Operator of the Second Kind on Einstein Manifolds
Haiqing Cheng, Kui Wang
In this note, we study Einstein manifolds whose curvature operator of the second kind satisfies the cone condition \[ α^{-1}\big(\sum_{i=1}^{[α]} λ_i+ (α- [α] ) λ_{[…
Einstein manifolds under cone conditions for the curvature operator of the second kind
Haiqing Cheng, Kui Wang
It is established in [6, 14, 23] that any closed Einstein manifold with two-nonnegative curvature operator of the second kind is either flat or a round sphere. In this paper, we re…
Einstein manifolds of negative lower bounds on curvature operator of the second Kind
Haiqing Cheng, Kui Wang
We demonstrate that -dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of satisfies $λ_1 \ge -θ(n) \barλ…
Schwarz symmetrizations in parabolic equations on complete manifolds
Haiqing Cheng, Tengfei Ma, Kui Wang
In this article, we prove a sharp estimate for the solutions to parabolic equations on manifolds. Precisely, using symmetrization techniques and isoperimetric inequalities on Riema…