發(fā)布時(shí)間：2018-06-04 09:08

  本文選題：凸體 + 星體�。� 參考：《西南大學(xué)》2017年碩士論文

【摘要】：經(jīng)典的Brunn-Minkowski理論起源于H.Brunn的博士論文和H.Minkowski的開創(chuàng)性工作.經(jīng)過 Bonnesen,Santalo,Fenchel,Blaschke,Busemann 等人的推動(dòng),使得凸幾何理論日漸完善,成為一個(gè)單獨(dú)的幾何研究分支.而在1975年Lutwak發(fā)表的《Dual Mixed Volumes》一文中首次定義了星體,建立了與凸體相對(duì)應(yīng)的對(duì)偶Brunn-Minkowski理論.對(duì)偶理論的建立,對(duì)解決Busemann-Petty問題有跨時(shí)代的意義.自20世紀(jì)80年代以來,凸體理論與星體理論的建立,使幾何學(xué)家們對(duì)凸幾何的研究取得重大成果,如 Lp-Brunn-Minkowski 和 Oricz-Brunn-Minkowski 理論.本文第一部分和第二部分介紹了研究背景和文中所需要的預(yù)備知識(shí).本文第三部分和第四部分是文章的主旨內(nèi)容,主要探究了混合相交體的Brunn-Minkowski理論中的不等式.在第三部分運(yùn)用Polya-Szego不等式和Holder不等式證明了混合相交體均質(zhì)積分的逆向Minkowski不等式,在此基礎(chǔ)上將系數(shù)0≤i≤n,0≤j≤n-1擴(kuò)充到0≤i,0≤j上.在第四部分運(yùn)用逆向的Minkowski不等式證明了混合相交體對(duì)偶均質(zhì)積分的逆向Brunn-minkowski不等式.
[Abstract]:The classical Brunn-Minkowski theory originates from H.Brunn 's doctoral thesis and H.Minkowski 's pioneering work. By Bonnesenn Santalofencheln Blaschkeke Busemann et al., the convex geometry theory is becoming more and more perfect and becomes a separate branch of geometry research. In 1975, Lutwak published "Dual Mixed Volumes" for the first time, defining stars and establishing the dual Brunn-Minkowski theory corresponding to convex bodies. The establishment of duality theory has a cross-epoch significance for solving Busemann-Petty problem. Since the eighties of the 20th century, the establishment of convex body theory and star theory has made great achievements in the research of convex geometry by geometrists, such as Lp-Brunn-Minkowski and Oricz-Brunn-Minkowski theory. The first and second parts of this paper introduce the research background and the preparatory knowledge needed in the paper. The third and fourth parts of this paper are the main content of the paper, mainly to explore the inequalities in the Brunn-Minkowski theory of mixed intersections. In the third part, Polya-Szego inequality and Holder inequality are used to prove the inverse Minkowski inequality for homogeneous integrals of mixed intersecting bodies. On this basis, the coefficient 0 鈮，

本文編號(hào)：1976808