The capture and transformation of the greenhouse gas CO_(2) into high-value products is currently of paramount importance worldwide,with many different approaches being conceived and tested[1-6].The transformation CO_...
THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ...
THIS is the last one of a series of three papers. Here, we discuss six topics related to the spectral gap: the gradient estimate, the heat kernel and Harnack inequality, the logarithmic Sobolev inequality, the converg...
THIS is the first of a series of three reviews. They are partially surveys on three aspects: (ⅰ) explaining the main ideas of our recent application of the coupling method to the estimation of spectral gap, (ⅱ) intr...
morphism. Harmonic morphisms may be characterized as harmonic mappings which are horizontally weakly conformal. In recent years a substantial progress has been made in the field of harmonic morphism, for example, refs...
Huisken proved that any hypersurface M0 satisfying a suitable convexity conditionin a Riemannian manifold contracts to a simple point during the evolution along its meancurvature vector. In this letter the ...
Project supported by the National Natural Science Foundation of China.
Let E be a real Hilbert space, λ∈R, F∈C^2(E×R, R). Suppose that the gradientD_xF(x,λ) of F is A(λ)x+N(x, λ), where N(x, λ) =o(│x│) as x→θ uniformly for bounded λ.In this note we consider the solutions of ...
A foundamental problem in 4-dimensional differential topology iS to find a surface with minimal genus that can represent a given two-dimensional homology class. Hsiang, Rohlin have got some results about the homologic...
Project partly supported by the National Natural Science Foundation of China and the State Education Commission of China.
Let (M, g) be a complete Riemannian manifold of dimension d and Ricci curvaturebounded below by-K for some K∈. Let dx and p(x,y) be respectively the Riemannianvolum element and Riemannian distance. Consider L=△+...