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Flows Associated to Cameron-martin Type Vector Fields on Path Spaces Over a riemannian manifold

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 499-508页

作者： Jing-xiao ZHANG Center for Applied Statistics School of StatisticsRenmin University of China

The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a riemannian manifold.

关键词： flow Cameron-Martin type vector field path space riemannian manifold

Every Sub-riemannian manifold Is the Gromov–Hausdorff Limit of a Sequence riemannian manifolds

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Acta Mathematica Sinica,English Series 2017年第11期33卷 1565-1568页

作者： Yong Hong HUANG School of Mathematical Science Capital Normal UniversityBeijing 100048P.R.China Qiannan Preschool Education College for Nationalities Guiding County of Guizhou Province558000P.R.China

In this paper, we will show that every sub-riemannian manifold is the Gromov-Hausdorff limit of a sequence of riemannian manifolds.

关键词： riemannian manifold Sub-riemannian manifold Gromov-Hausdorff convergence

Gradient Estimates for a Nonlinear Heat Equation on Compact riemannian manifold

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Journal of Mathematical Research with Applications 2012年第6期32卷 743-753页

作者： Xinrong JIANG1,2, , Caisheng LIAO21. Institute of Mathematics and Information Science, Jiangxi Normal University,Jiangxi 330022, P. R. China 2. Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China Institute of Mathematics and Information Science Jiangxi Normal University Jiangxi 330022 Department of Mathematics East China Normal University Shanghai 200241

In this paper, we study gradient estimates for the nonlinear heat equation ut △u =au log u, on compact riemannian manifold with or without boundary. We get a Hamilton type gradient estimate for the positive smooth solution to the equation on close manifold, and obtain a Li-Yau type gradient estimate for the positive smooth solution to the equation on compact manifold with nonconvex boundary.

关键词： nonlinear heat equation riemannian manifold gradient estimates.

Well-Posedness of Stochastic Continuity Equations on riemannian manifolds

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Chinese Annals of Mathematics,Series B 2024年第1期45卷 81-122页

作者： Luca GALIMBERTI Kenneth H.KARLSEN Department of Mathematical Sciences NTNU Norwegian University of Science and TechnologyN-7491 TrondheimNorway Department of mathematics University of OsloP.O.Box 1053BlindernN-0316 OsloNorway

The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed riemannian manifold M with metric *** velocity field u is perturbed by Gaussian noise terms Wi(t),:WN(t)driven by smooth spatially dependent vector fields a1(x),...,aN(x)on *** velocity u belongs to L_(t)^(1)W_(x)^(1,2)with divh u bounded in Lf,for p>d+2,where d is the dimension of M(they do not assume div_(h) u∈L_(t,x)^(∞)).For carefully chosen noise vector fields ai(and the number N of them),they show that the initial-value problem is well-posed in the class of weak L^(2) solutions,although the problem can be ill-posed in the deterministic case because of concentration *** proof of this“regularization by noise”result is based on a L^(2) estimate,which is obtained by a duality method,and a weak compactness argument.

关键词： Stochastic continuity equation riemannian manifold Hyperbolic equa-tion Non-smooth velocity field Weak solution Existence Uniqueness

Optimality Conditions on riemannian manifold of Nonsmooth Unconstrained Optimization

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Optimality Conditions on Riemannian Manifold of Nonsmooth Un...

An Interpolation of Hardy Inequality and Moser–Trudinger Inequality on riemannian manifolds with Negative Curvature

第十一届中国青年信息与管理学者大会

作者： Leifu Gao,Weiwei Fu Institute of Mathematics and Systems Science,Liaoning Technical University

＜正＞Defined Penot generalized directional Derivative of Lipschitz function on riemannian manifold using generalized directional derivative and generalized gradient determined optimality conditions on riemannian mani... 详细信息

关键词： riemannian manifold nonsmooth optimization optimality conditions generalized directional derivative generalized gradient

来源： cnki会议评论

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Acta Mathematica Sinica,English Series 2016年第7期32卷 856-866页

作者： Yan Qing DONG Qiao Hua YANG School of Mathematics and Statistics Wuhan University

Let M be a complete, simply connected riemannian manifold with negative curvature. We obtain an interpolation of Hardy inequality and Moser-Trudinger inequality on M. Furthermore, the constant we obtain is sharp.

关键词： Moser-Trudinger inequality Hardy inequality riemannian manifold negative curvature

Hamilton's Gradient Estimate for a Nonlinear Parabolic Equation on riemannian manifolds

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Journal of Mathematical Research with Applications 2015年第4期35卷 435-447页

作者： Xinrong JIANG Caisheng LIAO Institute of Mathematics and Information Science Jiangxi Normal University Department of Mathematics East China Normal University

In this paper,we give a local Hamilton’s gradient estimate for a nonlinear parabolic equation on riemannian *** its application,a Harnack-type inequality and a Liouville-type theorem are obtained.

关键词： Hamilton’s gradient estimate nonlinear parabolic equation riemannian manifold

An Estimate on riemannian manifolds of Dimension 4

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Analysis in Theory and Applications 2016年第3期32卷 272-282页

作者： Samy Skander Bahoura Departement de Mathematiques Universite Pierre et Marie Curie

We give an estimate of type sup x inf on riemannian manifold of dimension 4 for a Yamabe type equation.

关键词： sup x inf riemannian manifold dimension 4

The First Initial Boundary Value Problem for Parabolic Hessian Equations on riemannian manifolds

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Communications in Mathematical Research 2013年第4期29卷 305-319页

作者： Ren Chang-yu Yin Jing-xue School of Mathematics Jilin University

For a class of elliptic Hessian operators, one type of corresponding parabolic Hessian equations is studied on riemannian manifolds. uniqueness of the admissible solution to the first initial boundary the equations ar... 详细信息

关键词： Hessian operator fully nonlinear riemannian manifold