Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 899 - 916 |
| Number of pages | 18 |
| Journal | Journal of the American Mathematical Society |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 |
| Externally published | Yes |
Cite this
}
Proof of the fundamental gap conjecture. / Andrews, Ben; Clutterbuck, Julie Faye.
In: Journal of the American Mathematical Society, Vol. 24, No. 3, 2011, p. 899 - 916.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Proof of the fundamental gap conjecture
AU - Andrews, Ben
AU - Clutterbuck, Julie Faye
PY - 2011
Y1 - 2011
N2 - We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrodinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero potential. More generally, for an arbitrary smooth potential in higher dimensions, our proof gives both a sharp lower bound for the spectral gap and a sharp modulus of concavity for the logarithm of the first eigenfunction, in terms of the diameter of the domain and a modulus of convexity for the potential.
AB - We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrodinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero potential. More generally, for an arbitrary smooth potential in higher dimensions, our proof gives both a sharp lower bound for the spectral gap and a sharp modulus of concavity for the logarithm of the first eigenfunction, in terms of the diameter of the domain and a modulus of convexity for the potential.
UR - http://www.ams.org/journals/jams/2011-24-03/S0894-0347-2011-00699-1/S0894-0347-2011-00699-1.pdf
U2 - 10.1090/S0894-0347-2011-00699-1
DO - 10.1090/S0894-0347-2011-00699-1
M3 - Article
VL - 24
SP - 899
EP - 916
JO - Journal of the American Mathematical Society
JF - Journal of the American Mathematical Society
SN - 0894-0347
IS - 3
ER -