Desingularizing isolated conical singularities: Uniform estimates via weighted Sobolev spaces
Desingularizing isolated conical singularities: Uniform estimates via weighted Sobolev spaces
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去奇异化孤立的圆锥奇点：通过加权索博列夫空间进行统一估计
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
T. Pacini
中科院分区：
文献类型：
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作者：
T. Pacini
我们定义了一个非常一般的“参数连通和”构造，它可以用来消除黎曼流形的孤立锥奇点。然后，我们表明，各种重要的分析和椭圆估计，制定加权Sobolev空间，可以独立的参数中使用的建设。具体地说，我们证明了与（i）Sobolev嵌入定理，（ii）拉普拉斯算子的可逆性和（iii）Poincare和Gagliardo-Nirenberg-Sobolev型不等式有关的一致估计.
我们的主要工具是著名的理论加权Sobolev空间和椭圆算子的“锥”。我们提供了一个概述，连同前一般黎曼流形的延伸。
对于我们的结果的几何应用，我们请读者参考我们的论文“特殊拉格朗日锥，II：胶合结构在C^m”。
We define a very general "parametric connect sum" construction which can be used to eliminate isolated conical singularities of Riemannian manifolds. We then show that various important analytic and elliptic estimates, formulated in terms of weighted Sobolev spaces, can be obtained independently of the parameters used in the construction. Specifically, we prove uniform estimates related to (i) Sobolev Embedding Theorems, (ii) the invertibility of the Laplace operator and (iii) Poincare' and Gagliardo-Nirenberg-Sobolev type inequalities.
Our main tools are the well-known theories of weighted Sobolev spaces and elliptic operators on "conifolds". We provide an overview of both, together with an extension of the former to general Riemannian manifolds.
For a geometric application of our results we refer the reader to our paper "Special Lagrangian conifolds, II: Gluing constructions in C^m".