TY - JOUR
T1 - Equidistribution of minimal hypersurfaces for generic metrics
AU - Marques, Fernando C.
AU - Neves, André
AU - Song, Antoine
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/5/1
Y1 - 2019/5/1
N2 - For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mn+1, 3 ≤ (n+ 1) ≤ 7 , we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3):963–972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich et al. (Ann Math 187(3):933–961, 2018).
AB - For almost all Riemannian metrics (in the C∞ Baire sense) on a closed manifold Mn+1, 3 ≤ (n+ 1) ≤ 7 , we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3):963–972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich et al. (Ann Math 187(3):933–961, 2018).
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U2 - 10.1007/s00222-018-00850-5
DO - 10.1007/s00222-018-00850-5
M3 - Article
AN - SCOPUS:85059534496
SN - 0020-9910
VL - 216
SP - 421
EP - 443
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -