References of "Li, Yi 50025761"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailLi-Yau Harnack Estimates for a Heat-Type Equation Under the Geometric Flow
Li, Yi UL; Zhu, Xiaorui

in Potential Analysis (2018)

Detailed reference viewed: 126 (12 UL)
Full Text
Peer Reviewed
See detailHarnack estimates for a nonlinear parabolic equation under Ricci flow
Li, Yi UL; Zhu, Xiaorui

in Differential Geometry & its Applications (2018), 56

In this paper, we consider the Harnack estimates for a nonlinear parabolic equation under the Ricci flow. The gradient estimates for positive solutions as well as Li-Yau type inequalities are also given.

Detailed reference viewed: 201 (22 UL)
Full Text
See detailLocal curvature estimates for the Laplacian flow
Li, Yi UL

E-print/Working paper (2018)

Detailed reference viewed: 77 (8 UL)
Full Text
Peer Reviewed
See detailLong time existence and bounded scalar curvature in the Ricci-harmonic flow
Li, Yi UL

in Journal of Differential Equations (2018), 265(1), 69-97

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we ... [more ▼]

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the ``Riemann curvature'' for the Ricci-harmonic flow generalizing a recently result of Simon \cite{Simon2015}. [less ▲]

Detailed reference viewed: 168 (17 UL)
Full Text
See detailLocal curvature estimates for the Ricci-harmonic flow
Li, Yi UL

in Math ArXiv (2018)

In this paper we give an explicit bound of Δ_g(t)u(t)and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second ... [more ▼]

In this paper we give an explicit bound of Δ_g(t)u(t)and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second part these local curvature estimates are extended to a class of generalized Ricci flow, introduced by the author \cite{LY1}, whose stable points give Ricci-flat metrics on a complete manifold, and which is very close to the (K,N)-super Ricci flow recently defined by Xiangdong Li and Songzi Li \cite{LL2014}. Next we propose a conjecture for Einstein's scalar field equations motivated by a result in the first part and the bounded L^2-curvature conjecture recently solved by Klainerman, Rodnianski and Szeftel \cite{KRS2015}. In the last two parts of this paper, we discuss two notions of "Riemann curvature tensor" in the sense of Wylie-Yeroshkin \cite{KW2017, KWY2017, Wylie2015, WY2016}, respectively, and Li \cite{LY3}, whose "Ricci curvature" both give the standard Bakey-\'Emery Ricci curvature \cite{BE1985}, and the forward and backward uniqueness for the Ricci-harmonic flow. [less ▲]

Detailed reference viewed: 60 (3 UL)
Full Text
See detailHarnack estimates for nonlinear parabolic equations under the Ricci flow
Li, Yi UL; Zhu, Xiaorui

E-print/Working paper (2017)

In this paper, we consider first the Li-Yau Harnack estimates for a nonlinear parabolic equation $\partial_{t}u=\Delta_{t}u-qu -au(\ln u)^{\alpha}$ under the Ricci flow, where $\alpha>0$ is a constant. To ... [more ▼]

In this paper, we consider first the Li-Yau Harnack estimates for a nonlinear parabolic equation $\partial_{t}u=\Delta_{t}u-qu -au(\ln u)^{\alpha}$ under the Ricci flow, where $\alpha>0$ is a constant. To extend these estimates to a more general situation, in the second part, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation $\partial _{t}u=\Delta _{t}u+hu^{p}$ on a Riemannian manifold whose metrics evolve under the geometric flow $\partial _{t}g(t)=-2S_{g(t)}$. To obtain these estimates, we introduce a quantity $\underline{\boldsymbol{S}}$ along the flow which measures whether the tensor $S_{ij}$ satisfies the second contracted Bianchi identity. Under conditions on ${\rm Ric}_{g(t)}, S_{g(t)}$, and $\underline{\boldsymbol{S}}$, we obtain the gradient estimates. [less ▲]

Detailed reference viewed: 43 (4 UL)
Full Text
See detailGeneralized Ricci flow II: Existence for complete noncompact manifolds
Li, Yi UL

E-print/Working paper (2017)

Detailed reference viewed: 191 (18 UL)
Full Text
Peer Reviewed
See detailLong time existence of Ricci-harmonic flow
Li, Yi UL

in Frontiers of Mathematics in China (2016), 11(5), 1313-1334

We give a survey about recent results on Ricci-harmonic flow

Detailed reference viewed: 105 (14 UL)
Full Text
Peer Reviewed
See detailHarnack estimates for a heat-type equation under the Ricci flow
Li, Yi UL; Zhu, Xiaorui

in Journal of Differential Equations (2016), 260(4), 3270-3301

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two ... [more ▼]

In this paper, we consider the gradient estimates for a positive solution of the nonlinear parabolic equation ∂tu=Δtu+hup∂tu=Δtu+hup on a Riemannian manifold whose metrics evolve under the Ricci flow. Two Harnack inequalities and other interesting results are obtained. [less ▲]

Detailed reference viewed: 119 (12 UL)
Full Text
Peer Reviewed
See detailA geometric heat flow for vector fields
Li, Yi UL; Liu, KeFeng

in Science China Mathematics (2015), 58(4), 673-688

We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of ... [more ▼]

We introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution to this flow, discuss its convergence and possible applications, and its relation to the Navier-Stokes equations on manifolds and Kazdan-Warner-Bourguignon-Ezin identity for conformal Killing vector fields. We also provide two new criterions on the existence of Killing vector fields. A similar flow to finding holomorphic vector fields on Kähler manifolds will be studied by Li and Liu [less ▲]

Detailed reference viewed: 66 (4 UL)
Full Text
Peer Reviewed
See detailLi-Yau-Hamilton estimates and Bakry-Emery-Ricci curvature
Li, Yi UL

in Nonlinear Analysis: Theory, Methods & Applications (2015), 113

In this paper we derive Cheng–Yau, Li–Yau, Hamilton estimates for Riemannian manifolds with Bakry–Emery–Ricci curvature bounded from below, and also global and local upper bounds, in terms of ... [more ▼]

In this paper we derive Cheng–Yau, Li–Yau, Hamilton estimates for Riemannian manifolds with Bakry–Emery–Ricci curvature bounded from below, and also global and local upper bounds, in terms of Bakry–Emery–Ricci curvature, for the Hessian of positive and bounded solutions of the weighted heat equation on a closed Riemannian manifold. [less ▲]

Detailed reference viewed: 87 (7 UL)
Full Text
Peer Reviewed
See detailOn an extension of the H^k mean curvature flow of closed convex hypersurfaces
Li, Yi UL

in Geometriae Dedicata (2014), 172(1), 147-154

Detailed reference viewed: 35 (2 UL)
Full Text
Peer Reviewed
See detailLi-Yau estimates for a nonlinear parabolic equation on manifolds
Li, Yi UL; Zhu, Xiaorui

in Mathematical Physics, Analysis and Geometry (2014)

Detailed reference viewed: 53 (2 UL)
Full Text
Peer Reviewed
See detailEigenvalues and entropies under the harmonic-Ricci flow
Li, Yi UL

in Pacific Journal of Mathematics (2014), 267(1), 141-184

Detailed reference viewed: 48 (4 UL)
Full Text
Peer Reviewed
See detailMabuchi and Aubin-Yau functionals over complex surfaces
Li, Yi UL

in Journal of Mathematical Analysis and Applications (2014), 416(1), 81-98

Detailed reference viewed: 57 (1 UL)
Full Text
Peer Reviewed
See detailA priori estimates for Donaldson's equation over compact Hermitian manifolds
Li, Yi UL

in Calculus of Variations & Partial Differential Equations (2014), 50(3-4), 867-882

Detailed reference viewed: 48 (3 UL)
Full Text
Peer Reviewed
See detailOn an extension of the H^k n curvature flow
Li, Yi UL

in Science China Mathematics (2012), 55(1), 99-118

Detailed reference viewed: 25 (4 UL)
Full Text
Peer Reviewed
See detailGeneralized Ricci flow I: Higher-derivative estimates for compact manifolds
Li, Yi UL

in Analysis & PDE (2012), 5(4), 747-775

Detailed reference viewed: 69 (6 UL)
Full Text
Peer Reviewed
See detailHarnack inequality for the negative power Gaussian curvature flow
Li, Yi UL

in Proceedings of the American Mathematical Society (2011), 139(10), 3070-3717

Detailed reference viewed: 68 (3 UL)
Full Text
Peer Reviewed
See detailMabuchi and Aubin-Yau functionals over complex manifolds
Li, Yi UL

E-print/Working paper (2010)

Detailed reference viewed: 31 (3 UL)