scholarly journals Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian

2010 ◽  
Vol 19 (3-4) ◽  
pp. 735-809 ◽  
Author(s):  
D. Le Peutrec
Keyword(s):  
Witten Laplacian ◽  
Small Eigenvalues

scholarly journals WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY

2021 ◽  
pp. 1-38
Author(s):  
Xianzhe Dai ◽  
Junrong Yan
Keyword(s):  
Essential Role ◽  
Morse Function ◽  
Noncompact Manifold ◽  
Morse Inequalities ◽  
Bounded Geometry ◽  
Noncompact Manifolds ◽  
Witten Laplacian ◽  
Relative Cohomology ◽  
Witten Deformation ◽  
Small Eigenvalues

Abstract Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting.

Small eigenvalues on Riemann surfaces of genus 2

1991 ◽  
Vol 106 (1) ◽  
pp. 121-138 ◽  
Author(s):  
Paul Schmutz
Keyword(s):  
Riemann Surfaces ◽  
Genus 2 ◽  
Small Eigenvalues

scholarly journals Resurgent Analysis of the Witten Laplacian in One Dimension

2011 ◽  
Vol 54 (3) ◽  
pp. 383-438 ◽  
Author(s):  
Alexander Getmanenko
Keyword(s):  
One Dimension ◽  
Witten Laplacian ◽  
Resurgent Analysis

Errata: Small Eigenvalues of Large Hankel Matrices

1968 ◽  
Vol 19 (6) ◽  
pp. 1508
Author(s):  
Harold Widom ◽  
Herbert Wilf
Keyword(s):  
Hankel Matrices ◽  
Small Eigenvalues

EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW

2017 ◽  
Vol 59 (3) ◽  
pp. 743-751
Author(s):  
SHOUWEN FANG ◽  
FEI YANG ◽  
PENG ZHU
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Ricci Flow ◽  
Compact Riemannian Manifold ◽  
Laplacian Operator ◽  
Witten Laplacian ◽  
Normalized Ricci Flow ◽  
Geometric Operator

AbstractLet (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Ricci flow. In the paper, we prove that the eigenvalues of geometric operator −Δφ + $\frac{R}{2}$ are non-decreasing under the Ricci flow for manifold M with some curvature conditions, where Δφ is the Witten Laplacian operator, φ ∈ C2(M), and R is the scalar curvature with respect to the metric g(t). We also derive the evolution of eigenvalues under the normalized Ricci flow. As a consequence, we show that compact steady Ricci breather with these curvature conditions must be trivial.

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