tailieunhanh - báo cáo hóa học:" Research Article On Isoperimetric Inequalities in Minkowski Spaces"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Isoperimetric Inequalities in Minkowski Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 697954 18 pages doi 2010 697954 Research Article On Isoperimetric Inequalities in Minkowski Spaces Horst Martini1 and Zokhrab Mustafaev2 1 Faculty of Mathematics University of Technology Chemnitz 09107 Chemnitz Germany 2 Department of Mathematics University of Houston-Clear Lake Houston TX 77058 USA Correspondence should be addressed to Horst Martini Received 11 July 2009 Revised 2 December 2009 Accepted 4 March 2010 Academic Editor Ulrich Abel Copyright 2010 H. Martini and Z. Mustafaev. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The purpose of this expository paper is to collect some mainly recent inequalities conjectures and open questions closely related to isoperimetric problems in real finite-dimensional Banach spaces Minkowski spaces . We will also show that in a way Steiner symmetrization could be used as a useful tool to prove Petty s conjectured projection inequality. 1. Introductory General Survey In Geometric Convexity but also beyond its limits isoperimetric inequalities have always played a central role. Applications of such inequalities can be found in Stochastic Geometry Functional Analysis Fourier Analysis Mathematical Physics Discrete Geometry Integral Geometry and various further mathematical disciplines. We will present a survey on isoperimetric inequalities in real finite-dimensional Banach spaces also called Minkowski spaces. In the introductory part a very general survey on this topic is given where we refer to historically important papers and also to results from Euclidean geometry that are potential to be extended to Minkowski geometry that is to the geometry of Minkowski spaces of dimension d 2. The second part of the introductory .