References of "Li, Yi 50025761"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 23 1 2     Li-Yau Harnack Estimates for a Heat-Type Equation Under the Geometric FlowLi, Yi ; Zhu, Xiaoruiin Potential Analysis (2018)Detailed reference viewed: 143 (12 UL) Harnack estimates for a nonlinear parabolic equation under Ricci flowLi, Yi ; Zhu, Xiaoruiin Differential Geometry & its Applications (2018), 56In 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: 216 (22 UL) Local curvature estimates for the Ricci-harmonic flowLi, Yi 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: 65 (3 UL) Long time existence and bounded scalar curvature in the Ricci-harmonic flowLi, Yi in Journal of Differential Equations (2018), 265(1), 69-97In 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: 182 (17 UL) Local curvature estimates for the Laplacian flowLi, Yi E-print/Working paper (2018)Detailed reference viewed: 88 (8 UL) Harnack estimates for nonlinear parabolic equations under the Ricci flowLi, Yi ; Zhu, XiaoruiE-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: 46 (4 UL) Generalized Ricci flow II: Existence for complete noncompact manifoldsLi, Yi E-print/Working paper (2017)Detailed reference viewed: 209 (18 UL) Long time existence of Ricci-harmonic flowLi, Yi in Frontiers of Mathematics in China (2016), 11(5), 1313-1334We give a survey about recent results on Ricci-harmonic flowDetailed reference viewed: 120 (14 UL) Harnack estimates for a heat-type equation under the Ricci flowLi, Yi ; Zhu, Xiaoruiin Journal of Differential Equations (2016), 260(4), 3270-3301In 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: 135 (12 UL) A geometric heat flow for vector fieldsLi, Yi ; Liu, KeFengin Science China Mathematics (2015), 58(4), 673-688We 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: 81 (4 UL) Li-Yau-Hamilton estimates and Bakry-Emery-Ricci curvatureLi, Yi in Nonlinear Analysis: Theory, Methods & Applications (2015), 113In 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: 110 (7 UL) On an extension of the H^k mean curvature flow of closed convex hypersurfacesLi, Yi in Geometriae Dedicata (2014), 172(1), 147-154Detailed reference viewed: 37 (2 UL) Mabuchi and Aubin-Yau functionals over complex surfacesLi, Yi in Journal of Mathematical Analysis and Applications (2014), 416(1), 81-98Detailed reference viewed: 71 (1 UL) A priori estimates for Donaldson's equation over compact Hermitian manifoldsLi, Yi in Calculus of Variations & Partial Differential Equations (2014), 50(3-4), 867-882Detailed reference viewed: 62 (3 UL) Eigenvalues and entropies under the harmonic-Ricci flowLi, Yi in Pacific Journal of Mathematics (2014), 267(1), 141-184Detailed reference viewed: 63 (4 UL) Li-Yau estimates for a nonlinear parabolic equation on manifoldsLi, Yi ; Zhu, Xiaoruiin Mathematical Physics, Analysis and Geometry (2014)Detailed reference viewed: 70 (2 UL) On an extension of the H^k n curvature flowLi, Yi in Science China Mathematics (2012), 55(1), 99-118Detailed reference viewed: 29 (4 UL) Generalized Ricci flow I: Higher-derivative estimates for compact manifoldsLi, Yi in Analysis & PDE (2012), 5(4), 747-775Detailed reference viewed: 83 (6 UL) Harnack inequality for the negative power Gaussian curvature flowLi, Yi in Proceedings of the American Mathematical Society (2011), 139(10), 3070-3717Detailed reference viewed: 91 (3 UL) Mabuchi and Aubin-Yau functionals over complex three-foldsLi, Yi E-print/Working paper (2010)Detailed reference viewed: 38 (1 UL) 1 2