The Dirac operator under collapse to a smooth limit space
The Dirac operator under collapse to a smooth limit space
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塌缩到光滑极限空间下的狄拉克算子
DOI：
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发表时间：
2018
影响因子：
0.7
通讯作者：
Saskia Roos
中科院分区：
文献类型：
--
作者：
Saskia Roos
设（Mi,gi）i∈Ndocumentclass[12pt]{minimal} useppackageamsmath{ useppackageamsfonts }useppackageamssymb{ useppackageamssyb} useppackageamssys{ useppackageamssfs} useppackageams{希腊}setlengthoddsidemargin{-69pt} {egindocument}{}{}{}{}$$(M_i, g_i)_{i in mathbb {N}}$$ enddocument是一个具有均匀有界曲率和直径的自旋流形{序列}，该序列收敛于Gromov-Hausdorff拓扑中的低维riemann流形（B, h）。然后，Dirac算子的谱收敛于某一阶椭圆微分算子的谱。DBdocumentclass[12pt]minimal {useppackageamsmath }useppackagewasysym{ useppackageamsfonts} useppackageamssyb{ useppackageamssyb} useppackagemathrsfs{ useppackageupgreek }setlengthoddsidemargin{-69pt} egindocument {}{}{}{}{}{}$$mathcal {D}^B$$ enddocument在{b上}给出了{DBdocumentclass}[12pt]minimal useppackageamsmath useppackagewasysym {useppackageamsfonts}的显式描述{useppackageamssymb} useppackageamssy{ useppackagemathrsfs} useppackagemathrsfs {setlengthoddsidemargin}-69pt {egindocument}{}{}{}{}{}$$mathcal {D}^B$$ enddocument{并}描述{DBdocumentclass[12pt]最小}useppackageamsmath{ useppackagewasysym useppackageamsfonts }useppackageamssymb{ useppackageamssy useppackageamsfs} useppackageamssy{ setlengthoddsidemargin}-69pt{ egindocument }{}{}{}{}{}{}$$mathcal {D}^B$$ enddocument{等于B}上的Dirac操作符。
Let (Mi,gi)i∈Ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$(M_i, g_i)_{i in mathbb {N}}$$end{document} be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov–Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator DBdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathcal {D}^B$$end{document} on B. We give an explicit description of DBdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathcal {D}^B$$end{document} and characterize the special case where DBdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathcal {D}^B$$end{document} equals the Dirac operator on B.
狄拉克谱的连续性
影响因子：
0.7
作者：
N. Nowaczyk
通讯作者：
N. Nowaczyk