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

【摘要】：本文研究的內容屬于賦值理論.賦值理論是算子理論和凸幾何分析的交叉學科.凸幾何分析是現(xiàn)代幾何分析領域的一個重要分支,它在分析學,微分幾何,積分幾何,偏微分方程理論,信息論,隨機幾何,局部Banana空間理論等數(shù)學領域有著廣泛的應用.賦值理論起源于Dehn關于Hilbert第三問題的解答Hadwiger特征定理的完成標志著賦值理論正式成為系統(tǒng)的研究領域Hadwiger特征定理的應用給出了眾多關于幾何不變量的結果的簡單證明.在第一章,本文介紹了賦值理論的發(fā)展,并簡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備知識和通用記號.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當且僅當Orlicz賦值退化為Lp 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了SL(n)相容的L∞ Minkowski賦值Lp Minkowski賦值的分類基于我們對p齊次連續(xù)函數(shù)值賦值的分類.在第五章,本文研究了另外一種函數(shù)值賦值,刻畫了著名的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：1775190