The Weyl Law for the phase transition spectrum and density of limit interfaces
We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich–Marques–Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie–Marques–Neves and Marques–Neves–Son...
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| Published in | Geometric and functional analysis Vol. 29; no. 2; pp. 382 - 410 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.04.2019
Springer Nature B.V |
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| Abstract | We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich–Marques–Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie–Marques–Neves and Marques–Neves–Song, respectively. We also prove the density of
separating
limit interfaces for generic metrics in dimension 3, based on the recent work of Chodosh–Mantoulidis, and for generic metrics on manifolds containing only separating minimal hypersurfaces, e.g.
H
n
(
M
,
Z
2
)
=
0
, for
4
≤
n
+
1
≤
7
. These provide alternative proofs of Yau’s conjecture on the existence of infinitely many minimal hypersurfaces for generic metrics on each setting, using the Allen–Cahn approach. |
|---|---|
| AbstractList | We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich–Marques–Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie–Marques–Neves and Marques–Neves–Song, respectively. We also prove the density of separating limit interfaces for generic metrics in dimension 3, based on the recent work of Chodosh–Mantoulidis, and for generic metrics on manifolds containing only separating minimal hypersurfaces, e.g. Hn(M,Z2)=0, for 4≤n+1≤7. These provide alternative proofs of Yau’s conjecture on the existence of infinitely many minimal hypersurfaces for generic metrics on each setting, using the Allen–Cahn approach. We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich–Marques–Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie–Marques–Neves and Marques–Neves–Song, respectively. We also prove the density of separating limit interfaces for generic metrics in dimension 3, based on the recent work of Chodosh–Mantoulidis, and for generic metrics on manifolds containing only separating minimal hypersurfaces, e.g. H n ( M , Z 2 ) = 0 , for 4 ≤ n + 1 ≤ 7 . These provide alternative proofs of Yau’s conjecture on the existence of infinitely many minimal hypersurfaces for generic metrics on each setting, using the Allen–Cahn approach. |
| Author | Gaspar, Pedro Guaraco, Marco A. M. |
| Author_xml | – sequence: 1 givenname: Pedro surname: Gaspar fullname: Gaspar, Pedro organization: Department of Mathematics, The University of Chicago – sequence: 2 givenname: Marco A. M. surname: Guaraco fullname: Guaraco, Marco A. M. email: guaraco@math.uchicago.edu organization: Department of Mathematics, The University of Chicago |
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| Title | The Weyl Law for the phase transition spectrum and density of limit interfaces |
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