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We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential.
S.-T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math
1975
Earlier work this paper cites.
H. Brascamp and E. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Func. Anal
1976
Earlier work this paper cites.
P. Li, A lower bound for the first eigenvalue of the Laplacian on a compact manifold, Indiana Univ. Math. J
1979
Earlier work this paper cites.
P. Li and S.-T. Yau, Estimates of eigenvalues of a compact Riemannian manifold, AMS. Proc. Symp. Pure Math
1980
Cited alongside, same era.
J.Q. Zhong and H.C. Yang, On the estimate of the first eigenvalues of a compact Riemannian manifold, Sci. Sinica Ser. A
1984
Cited alongside, same era.
I.M. Singer, B. Wang, S.-T. Yau and S.S.-T. Yau, An estimate of the gap of the first two eigenvalues, Ann. Scuola Norm. Sup. Pisa. Cl. Sci
1985
Cited alongside, same era.
G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math/0211159
Cited in the paper.
N.J. Korevaar, Convexity properties of solutions to elliptic P.D.E.’s, Variational methods for free surface interfaces (Menlo Park, Calif., 1985)
1987
Later among the works it cites.
J. Ling, A lower bound for the gap between the first two eigenvalues of Schrödinger operators on the convex domain in S n S^{n} or R n R^{n} , Michigan Mathematical Journal
1993
Later among the works it cites.
S.-T. Yau, An estimate of the gap of the first two eigenvalues in the Schrödinger operator, Lectures on Partial differential equations: procedings in honor of Louis Nirenberg’s 75th Birthday
2003
Later among the works it cites.
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