从L_p Minkowski赋值到Orlicz赋值以及一般性的函数值赋值

发布时间：2018-04-19 23:20

  本文选题：赋值 + SL(n)协变　； 参考：《上海大学》2016年博士论文

【摘要】：本文研究的内容属于赋值理论.赋值理论是算子理论和凸几何分析的交叉学科.凸几何分析是现代几何分析领域的一个重要分支,它在分析学,微分几何,积分几何,偏微分方程理论,信息论,随机几何,局部Banana空间理论等数学领域有着广泛的应用.赋值理论起源于Dehn关于Hilbert第三问题的解答Hadwiger特征定理的完成标志着赋值理论正式成为系统的研究领域Hadwiger特征定理的应用给出了众多关于几何不变量的结果的简单证明.在第一章,本文介绍了赋值理论的发展,并简要介绍了本文得到的研究成果.在第二章,本文列出了一些必要的预备知识和通用记号.在第三章,本文研究了Orlicz赋值.我们证明了SL(n)相容(协变或反变)的Orlicz赋值具有非平凡的解时当且仅当Orlicz赋值退化为Lp Minkowski赋值.在第四章,本文研究了Lp Minkowski赋值,并且完全建立了多胞形上的SL(n)相容的Lp Minkowski赋值的分类定理.在此之前Ludwig, Haberl, Parapatits等人的成果都带了一些特殊条件.此外我们还完全分类了SL(n)相容的L∞ Minkowski赋值Lp Minkowski赋值的分类基于我们对p齐次连续函数值赋值的分类.在第五章,本文研究了另外一种函数值赋值,刻画了著名的Laplace变换.
[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，

本文编号：1775190