| 《几何分析手册(第2卷)》：The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics, as well as to aid in the learning of new mathematical topics by students all over the world. Each volume consists of either an expository monograph or a collection of signifi-cant introductions to important topics. This series emphasizes the history and sources of motivation for the topics under discussion, and also gives an over view of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics. Geometric Analysis combines differential equations and differential geometry. Animportant aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the laplace operator, many differential equations arising from differential geometry are nonlinear. Aparticularly important example is the Monge-Ampre equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis provides introductions to andsurveys of important topics in geometric analysis and their applications to related fields which is intend to be referred by graduate students and researchers in related areas. |
| heat kernels on metric measure spaces with regular volume growth 1 introduction 1.1 heat kernel in rn 1.2 heat kernels on riemannian manifolds 1.3 heat kernels of fractional powers of laplacian 1.4 heat kernels on fractal spaces 1.5 summary of examples 2 abstract heat kernels 2.1 basic definitions 2.2 the dirichlet form 2.3 identifying φ in the non-local case 2.4 volume of balls 3 besov spaces 3.1 besov spaces in irn 3.2 besov spaces in a metric measure space 3.3 embedding of besov spaces into hslder spaces 4 the energy domain 4.1 a local case 4.2 non-local case 4.3 subordinated heat kernel 4.4 bessel potential spaces 5 the walk dimension 5.1 intrinsic characterization of the walk dimension 5.2 inequalities for the walk dimension 6 two-sided estimates in the local case 6.1 the dirichlet form in subsets 6.2 maximum principles 6.3 a tail estimate 6.4 identifying φ in the local case references a convexity theorem and reduced delzant spaces 1 introduction 2 convexity of image of moment map 3 rationality of moment polytope 4 realizing reduced delzant spaces 5 classification of reduced delzant spaces references localization and some recent applications 1 introduction 2 localization 3 mirror principle 4 hori-vafa formula 5 the marifio-vafa conjecture 6 two partition formula 7 theory of topological vertex. 8 gopakumar-vafa conjecture and indices of elliptic operators 9 two proofs of the elsv formula 10 a localization proof of the wittcn conjecture 11 final remarks references gromov-witten invariants of toric calabi-yau threefolds 1 gromov-witten invariants of calabi-yau 3-folds 1.1 symplectic and algebraic gromov-wittcn invariants 1.2 moduli space of stable maps 1.3 gromov-witten invariants of compact calabi-yau 3-folds 1.4 gromov-witten invariants of noncompact calabi-yau 3-folds 2 traditional algorithm in the toric case 2.1 localization 2.2 hodge integrals 3 physical theory of the topological vertex 4 mathematical theory of the topological vertex 4.1 locally planar trivalent graph 4.2 formal toric calabi-yau (ftcy) graphs 4.3 degeneration formula 4.4 topological vertex 4.5 localization 4.6 framing dependence 4.7 combinatorial expression 4.8 applications 4.9 comparison 5 gw/dt correspondences and the topological vertex acknowledgments references survey on affine spheres convergence and collapsing theorems in riemannian geometry geometric transformations and soliton equations affine integral geometry from a differentiable viewpoint classification of fake projective planes |
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