Geometric Analysis and PDEs
This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The pr
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Matthew J. Gursky Ermanno Lanconelli Andrea Malchiodi
Gabriella Tarantello Xu-Jia Wang Paul C. Yang
Geometric Analysis and PDEs
1977 Cetraro, Italy 2007 Editors: Antonio Ambrosetti Sun-Yung Alice Chang Andrea Malchiodi y
5π 8
θ1
3π 8
Γ1t
1π 8
t
Γ2t x
L
9π 8
θ2
11 π 8
123
− 38 π
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1977
C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and cooperators the main purposes and the functioning of the Centre may be summarized as follows: every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each session is generally based on three or four main courses (24−30 hours over a period of 6-8 working days) held from specialists of international renown, plus a certain number of seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor just a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participation of the courses cover the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advance research in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first building brick in the edifice of international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Università di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]
C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica Università di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]
For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: – INdAM (Istituto Nationale di Alta Mathematica)
Matthew J. Gursky · Ermanno Lanconelli Andrea Malchiodi · Gabriella Tarantello Xu-Jia Wang · Paul C. Yang
Geometric Analysis and PDEs Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 11–16, 2007 Editors: Antonio Ambrosetti Sun-Yung Alice Chang Andrea Malchiodi
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Editors Alice Chang Princeton University Fine Hall Washington Road Princeton, NJ 085
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