| Geometric Analysis and Pdes: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 11-16, 2007 2009 Edition Contributor(s): Gursky, Matthew J. (Author), Ambrosetti, Antonio (Editor), Lanconelli, Ermanno (Author) |
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ISBN: 3642016731 ISBN-13: 9783642016738 Publisher: Springer OUR PRICE: $66.45 Product Type: Paperback Published: June 2009 Annotation: 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 presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Science | Physics - Mathematical & Computational - Mathematics | Mathematical Analysis |
| Dewey: 515.353 |
| Physical Information: 0.64" H x 6.14" W x 9.21" (0.94 lbs) 256 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This volume contains the notes of the lectures delivered at the CIME course GeometricAnalysis andPDEsduringtheweekofJune11-162007inCetraro (Cosenza). The school consisted in six courses held by M. Gursky (PDEs in Conformal Geometry), E. Lanconelli (Heat kernels in sub-Riemannian s- tings), A. Malchiodi(Concentration of solutions for some singularly perturbed Neumann problems), G. Tarantello (On some elliptic problems in the study of selfdual Chern-Simons vortices), X. J. Wang (Thek-Hessian Equation)and P. Yang (Minimal Surfaces in CR Geometry). Geometric PDEs are a ?eld of research which is currently very active, as it makes it possible to treat classical problems in geometry and has had a dramatic impact on the comprehension of three- and four-dimensional ma- folds in the last several years. On one hand the geometric structure of these PDEs might cause general di?culties due to the presence of some invariance (translations, dilations, choice of gauge, etc. ), which results in a lack of c- pactness of the functional embeddings for the spaces of functions associated with the problems. On the other hand, a geometric intuition or result might contribute enormously to the search for natural quantities to keep track of, andtoproveregularityoraprioriestimatesonsolutions. Thistwo-foldaspect of the study makes it both challenging and complex, and requires the use of severalre?nedtechniquestoovercomethemajordi?cultiesencountered. |