Covering lemmas and an application to nodal geometry on Riemannian manifolds

Lu, Guozhen

doi:10.1090/S0002-9939-1993-1160304-0

Covering lemmas and an application to nodal geometry on Riemannian manifolds
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Proc. Amer. Math. Soc. 117 (1993), 971-978 Request permission

Abstract:

The main part of this note is to show a general covering lemma in ${R^n},\;n \geqslant 2$, with the aim to obtain the estimate for BMO norm and the volume of a nodal set of eigenfunctions on Riemannian manifolds.

References

Sagun Chanillo and B. Muckenhoupt, Nodal geometry on Riemannian manifolds, J. Differential Geom. 34 (1991), no. 1, 85–91. MR 1114453
Harold Donnelly and Charles Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. Math. 93 (1988), no. 1, 161–183. MR 943927, DOI 10.1007/BF01393691
H. Donnelly and C. Fefferman, Growth and geometry of eigenfunctions of the Laplacian, Analysis and partial differential equations, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 635–655. MR 1044811
Guozhen Lu, Covering lemmas and BMO estimates for eigenfunctions on Riemannian surfaces, Rev. Mat. Iberoamericana 7 (1991), no. 3, 221–246. MR 1165070, DOI 10.4171/RMI/111
E. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), no. 4, 813–874. MR 1175693, DOI 10.2307/2374799