本文選題：賦值 + SL(n)協(xié)變��； 參考：《上海大學(xué)》2016年博士論文

【摘要】：本文研究的內(nèi)容屬于賦值理論.賦值理論是算子理論和凸幾何分析的交叉學(xué)科.凸幾何分析是現(xiàn)代幾何分析領(lǐng)域的一個(gè)重要分支,它在分析學(xué),微分幾何,積分幾何,偏微分方程理論,信息論,隨機(jī)幾何,局部Banana空間理論等數(shù)學(xué)領(lǐng)域有著廣泛的應(yīng)用.賦值理論起源于Dehn關(guān)于Hilbert第三問(wèn)題的解答Hadwiger特征定理的完成標(biāo)志著賦值理論正式成為系統(tǒng)的研究領(lǐng)域Hadwiger特征定理的應(yīng)用給出了眾多關(guān)于幾何不變量的結(jié)果的簡(jiǎn)單證明.在第一章,本文介紹了賦值理論的發(fā)展,并簡(jiǎn)要介紹了本文得到的研究成果.在第二章,本文列出了一些必要的預(yù)備知識(shí)和通用記號(hào).在第三章,本文研究了Orlicz賦值.我們證明了SL(n)相容(協(xié)變或反變)的Orlicz賦值具有非平凡的解時(shí)當(dāng)且僅當(dāng)Orlicz賦值退化為L(zhǎng)p Minkowski賦值.在第四章,本文研究了Lp Minkowski賦值,并且完全建立了多胞形上的SL(n)相容的Lp Minkowski賦值的分類(lèi)定理.在此之前Ludwig, Haberl, Parapatits等人的成果都帶了一些特殊條件.此外我們還完全分類(lèi)了SL(n)相容的L∞ Minkowski賦值Lp Minkowski賦值的分類(lèi)基于我們對(duì)p齊次連續(xù)函數(shù)值賦值的分類(lèi).在第五章,本文研究了另外一種函數(shù)值賦值,刻畫(huà)了著名的Laplace變換.
[Abstract]:The content of this paper belongs to assignment theory. Assignment theory is an interdisciplinary subject of operator theory and convex geometric analysis. Convex geometry analysis is an important branch of modern geometric analysis. It is widely used in the fields of analysis, differential geometry, integral geometry, partial differential equation theory, information theory, random geometry, local Banana space theory and so on. Assignment theory originated from Dehn's solution to Hilbert's third problem. The completion of Hadwiger's characteristic theorem indicates that assignment theory has become a systematic research field. The application of Hadwiger's characteristic theorem gives a lot of simple proofs of the results of geometric invariants. In the first chapter, this paper introduces the development of assignment theory, and briefly introduces the research results obtained in this paper. In the second chapter, this paper lists some necessary preparatory knowledge and general notation. In the third chapter, we study the Orlicz assignment. We prove that the Orlicz assignment of SLN) compatible (covariant or inverse) has a nontrivial solution if and only if the Orlicz assignment degenerates to LP Minkowski assignment. In chapter 4, we study LP Minkowski assignment, and completely establish the classification theorem of LP Minkowski assignment on polymorphic. Prior to this, Ludwig, Haberl, Parapatits and others have brought some special conditions. In addition, we completely classify the L 鈭，

本文編號(hào)：1775190