This publication examines holomorphic Morse inequalities and the asymptotic growth of the Bergman kernel on manifolds by utilizing the warmth kernel. It opens views on a number of energetic components of analysis in complicated, Kähler and symplectic geometry. various purposes also are incorporated, akin to an analytic evidence of Kodaira's embedding theorem, an answer of the Grauert-Riemenschneider and Shiffman conjectures, compactification of whole Kähler manifolds of pinched unfavourable curvature, Berezin-Toeplitz quantization, susceptible Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Read Online or Download Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics) PDF
Best Differential Geometry books
This publication is an exposition of the means of surgical procedure on simply-connected tender manifolds. Systematic research of differentiable manifolds utilizing those principles used to be began by way of Milnor  and Wallace  and built widely within the final ten years. it really is now attainable to offer a fairly whole concept of simply-connected manifolds of size ~ five utilizing this technique and that's what i'll try and start right here.
Thomas Cecil is a math professor with an unrivalled grab of Lie Sphere Geometry. the following, he presents a transparent and accomplished smooth therapy of the topic, in addition to its purposes to the research of Euclidean submanifolds. It starts off with the development of the gap of spheres, together with the elemental notions of orientated touch, parabolic pencils of spheres, and Lie sphere ameliorations.
This specific monograph by way of a famous UCLA professor examines intimately the math of Kerr black holes, which own the houses of mass and angular momentum yet hold no electric cost. compatible for complex undergraduates and graduate scholars of arithmetic, physics, and astronomy in addition to expert physicists, the self-contained remedy constitutes an creation to trendy thoughts in differential geometry.
"Brings to the reader a major volume of knowledge, good equipped and condensed into below 2 hundred pages. " — Mathematical ReviewsIn contemporary a long time twistor idea has turn into a major concentration for college kids of mathematical physics. imperative to twistor thought is the geometrical rework referred to as the Penrose remodel, named for its groundbreaking developer.
Extra info for Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics)