Averages of Eigenfunctions Over Hypersurfaces
Averages of Eigenfunctions Over Hypersurfaces
复制标题
超曲面本征函数的平均值
DOI：
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发表时间：
2017
影响因子：
2.4
通讯作者：
J. Toth
中科院分区：
文献类型：
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作者：
Y. Canzani;J. Galkowski;J. Toth
Let (M, g) be a compact, smooth, Riemannian manifold and {ϕh}documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${{ phi_h }}$$end{document} an L2-normalized sequence of Laplace eigenfunctions with defect measure μdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${mu}$$end{document}. Let H be a smooth hypersurface with unit exterior normal νdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$
u$$end{document}. Our main result says that when μdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mu$$end{document} is not concentrated conormally to H, the eigenfunction restrictions to H satisfy ∫HϕhdσH=o(1)and∫HhDνϕhdσH=o(1),documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$int_H phi_h dsigma_H = o(1) quad {
m and} quad int_H h D_{
u} phi_h dsigma_H = o(1),$$end{document}h→0+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${h o 0^+}$$end{document}.
