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Www I Mackicha N I Com/ Notices Mathematics from Hindawi l Discrete Dynamics in laa. ..a.. ..oo. , Nature and Society anrf.- .. ~--:· AMRX Applied Mathematics ,_-_ ..._ ... - Research express - 201MNumHrS http://aaa.hindawi.com http://ade.hindawi.com http://amrx.hindawi.com http://ddns.hindawi.com ISSN: 1085-3375 ISSN: 1687-1839 ISSN: 1687-1200 ISSN: 1026-0226 Volume 2005, 1000 ± Pages Volume 2005,400 ± Pages Volume 2005, 300 ± Pages Volume 2005,400± Pages Subscription Rate: $395 Subscription Rate: $195 Subscription Rate: $195 Subscription Rate: $195 Internationaf Joumar of IMRP mcrtfjematic5 IMRL. INTERNATIONAL an6 :roatl)enumcaf !;rum.. Mathematics Resean:h MATHEMATICS RESEARCH ------..-411 PAPERS ...... .....,...-~-..oil 2004 - ·-.. --~--- http://fpta.hindawi.com http://ijmms.hindawi.com http://imrn.hindawi.com http://imrp.hindawi.com ISSN: 1687-1 820 ISSN:0161-1712 ISSN: 1073-7928 ISSN: 1687-3017 Volume 2005,400 ±Pages Volume 2005,4000 ±Pages Volume 2005,4500 ±Pages Volume 2005,400 ±Pages Subscription Rate: $195 Subscription Rate: $995 Subscription Rate:$2395 Subscription Rate:$195 Mathematical I MRS JAMS A Problems in INTERNATIONAL MATHEMATICS Engineering RESEARCH SURVEYS Journal of Applied Mathematics and stochastic Analysis Theory, Methods. and Applications http://imrs.hindawi.com http://jam.hindawi.com http://ja msa.hindawi.com http://mpe.hindawi.com ISSN: 1687·1308 ISSN: 111 0-757X ISSN: 1048-9533 ISSN: 1024-123X Volume 2005,400 ± Pages Volume 2005,600 ±Pages Volume 2005,400± Pages Volume 2005,600 ± Pages Subscription Rate: $195 Subscription Rate: $295 Subscription Rate: $195 Subscription Rate: $295 --- ---- -- -- -- --- W JN 07\WJ Hindawi Publishing Corporation, 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA II F\ Fax: 1-866-446-3294 (USA, toll-free); URL: http://hindawi.com; E-mail: [email protected] ----- HTTp://www.HiNdAwi.coM/jouRNAls/iMRs/ IMR ~~~:. ~~~e1matione l Mathematics Research Surveys INTERNATIONAL MATHE RESEARCH SURVE Elliptic Equations of Yamabe Type Olivier Druet and Emmanuel Hebey Morris Weisfeld Editor-in-Chief Dedicated to Maximilien and Theophile [email protected]. edu Contents Nicolas Katz I. Introduction , ...... ....... nmk@m ath.princeton.edu 2. PDE background 3. Euclidean background . .. .. .. Terence Tao 4. The Yamabe problem 5. The negative case in Yamabe-type ~~-~~~~~~~ [email protected] 16 6. The H?-theory for blow-up . ..... ... ... ........... ..... 17 7. Uniqueness in the Hi -theory . ....... .... ..... 32 Vladimir Voevodsky 8. Examples of blowing-up s equences of solutions 37 [email protected] 9. TheC0-theotyforblow-up . .. ..... ..... .. : : : ::::: :· · ·· · · · · ·· 10. Proof of Theorem 9. 1 . 54 ·· ························· ·· 11 . Remark on the coercivity 58 82 12. The 3-dimensional case . ...... .. 85 13. Higher dimensions . ........ .. .. .. .... 90 14. Compactness and noncompactness 103 Eqitor-in-Chief 1 Introduction duke.edu Our ~im in ~his ~a per is to report on a current ly active research a rea in the field of eo­ weisfeld@math. metric partial differential equations (PDEs). We chose to report on the specific thea~ of Received I June 2004. Revision received 2 November 2004. General Information [email protected] Author Proposals · [email protected] We:report on th e specific theory of elliptic equations ofYamabe type. Such equations h ave been the ;:targe(of investigation for decades. Among other topics, we discuss the very complete H ~ -theory and t9-theofy for the blow-up of sequences of solutions of such equations. We also address the question oflhe1ocalizai~on of blow-up points, and discuss compactness and noncompactness issues. • . • 1 ~ 1N 07\WI Hindawi Pubhshmg Corporation, 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA; II t=\ Fax: 1 -866-446-3294 (USA, toll-free), URL: http.//www.hindawi.com, E -m ail. [email protected] NEW f6 NOTEWORTHY from Birkhiiuser Modern Differential Geometric Function Theory Geometric Problems on Geometry in Gauge Explorations in Complex Analysis Maxima and Minima Theories STEVEN G. KRANTZ, Washington University, St Louis, MO TITU ANDREESCU, University of Wisconsin, Whitewater, WI,· American Mathematics Competitions, University of Nebraska, Volume 1: Maxwell Fields Presented from the point of view of modern work in the field, this new book addresses advanced topics in Lincoln, NE; OLEG MUSHKAROV, Institute for Mathematics, ANASTASIOS MALLIOS, University of Athens complex analysis that verge on current areas of Bulgarian Academy of Sciences, Sofia; LUCHEZAR Panepistimioupolis, Athens, Greece STOYANOV, University of Western Australia, Crawley, Western research, including invariant geometry, the Bergman Australia Differential geometry, in the classical sense, is devel­ metric, the automorphism groups of domains, extremal oped through the theory of smooth manifolds. In the length, harmonic measure, boundary regularity of Reflecting the authors' experience as teachers and early 1990s, the author of this work initiated a new kind conformal maps, the Poisson kernel, the Hilbert Olympiad coaches, this carefully developed problem of differential geometry in which all the machinery of transform, the boundary behavior of harmonic and book takes a unique, intuitive approach to extreme­ classical differential geometry can be explained without holomorphic functions, the inhomogeneous value problems, treating them within the framework of any notion of smoothness. This was achieved via sheaf Cauchy-Riemann equations, and the corona problem. Euclidean geometry. Included is a comprehensive theory (geometry) and sheaf cohomology (analysis). The author adroitly weaves these varied topics to reveal selection of maxima and minima problems, from a number of delightful interactions. Perhaps more classical Greek constructions to modern open ques­ This two-volume work systematically applies the tions; detailed, step-by-step solutions to many of the author's sheaf-theoretic approach to such physical importantly, the topics are presented with an under­ standing and explanation of their interrelations with exercises are provided. The reader is exposed to theories as gauge theory. Both volumes contain a wealth algebra, analysis, combinatorics, and topology, and, of detailed and rigorous computations, and will appeal other important areas of mathematics such as harmonic analysis, differential geometry, partial differential throughout the text, emphasis is placed on creative to mathematicians and physicists as well as advanced techniques for problem solving. This volume is ideal for undergraduate and graduate students studying applica­ equations, potential theory, abstract algebra, and invariant theory. use at the junior and senior undergraduate level, as well tions of differential geometry to physical theories. as for enrichment programs and Olympiad training for 2005/APPROX. 450 PP./HARDCOVER 2005/APPROX. 350 PP., 20 ILLUS./HARDCOVER advanced high school students. ISBN O-BI76-437B-B/SI29 .00 (TENT.) ISBN O-BI76-4339-7 j$69.95 (TENT.) 2005/APPROX. 320 PP./SOFTCOVER PROGRESS IN MATHEMATICAL PHYSICS CORNERSTONES ISBN O-BI76-3517-3/S79.95 (TENT.) Volume 2: Yang-Mills Fields Differential Geometry and Differential Geometry of Continuing his point of view started in Volume I, the Analysis on CR Manifolds author extends the application of his sheaf-theoretic SORIN DRAGOMIR, Universitii della Basilicata, Romano, Curves and Surfaces approach to Yang-Mills fields in general. Important Potenza, Italy; GIUSEPPE TOMASSINI, Scuola Normale A Concise Guide topics covered include cohomological classification of Superiore, Pisa, Italy VICTOR A. TOPONOGOV, Sobolev Institute of Mathematics, Yang-Mills fields, the geometry of Yang-Mills A-connec­ This monograph is a unified presentation of several Novosibtrsk, Russia; VLADIMIR Y. ROVENSKI, Technion tions and moduli space of a vector sheaf, and Einstein's differential geometric aspects in the theory of CR Israel Institute of Technology, Haifa, Israel equation in a vacuum. manifolds and tangential Cauchy-Riemann equations. It This book presents traditional material of curves and 2005/APPROX. 360 PP./HARDCOVER presents topics from the Tanaka-Webster connection, a surfaces related to differential geometry along with ISBN O-BI76-4379-6/SI20.00 (TENT.) key contributor to the birth of pseudohermitian geome­ PROGRESS IN MATHEMATICAL PHYSICS important ideas of Riemannian geometry. The author try, to the major differential geometric achievements in introduces the reader to curves, then progresses to the theory of CR manifolds, such as Fefferman's metric, surfaces, and finally to more complex topics in the Finite Congruence Lattices pseudo-Einstein structures and the Lee conjecture, CR concluding section. The book weaves together standard of LaHices immersions, subelliptic harmonic maps as a local theoretical material with more difficult theorems and manifestation of pseudoharmonic maps from a CR complex problems while maintaining an easy separation GEORGE GRATZER, University of Manitoba, Winnipeg, manifold, Yang-Mills fields on CR manifolds, to name Canada between the two. One of the striking features of this several. It also aims at explaining how certain results presentation is the large number of nontrivial and In the past half-century the study of lattices has become from analysis are employed in CR geometry. original problems, some with useful hints and solutions, a large and important field with a great number of 2005/APPROX. 530 PP./HARDCOVER which introduce a motivated student into the real world interesting and deep results
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