scholarly journals Small eigenvalues of random 3-manifolds

2021 ◽  
Author(s):  
Ursula Hamenstädt ◽  
Gabriele Viaggi
Keyword(s):  
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

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

Estimating small eigenvalues of Riemann surfaces

1987 ◽  
pp. 93-121 ◽  
Author(s):  
Jozef Dodziuk ◽  
Thea Pignataro ◽  
Burton Randol ◽  
Dennis Sullivan
Keyword(s):  
Riemann Surfaces ◽  
Small Eigenvalues

scholarly journals Metastability and small eigenvalues in Markov chains

2000 ◽  
Vol 33 (46) ◽  
pp. L447-L451 ◽  
Author(s):  
Anton Bovier ◽  
Michael Eckhoff ◽  
Véronique Gayrard ◽  
Markus Klein
Keyword(s):  
Markov Chains ◽  
Small Eigenvalues

Uniqueness and critical spectrum of boundary spike solutions

2001 ◽  
Vol 131 (6) ◽  
pp. 1457-1480 ◽  
Author(s):  
Juncheng Wei
Keyword(s):  
Singularly Perturbed Problem ◽  
Curvature Function ◽  
Exact Asymptotics ◽  
Degenerate Critical Point ◽  
Spike Solution ◽  
Critical Spectrum ◽  
The Mean ◽  
Image Position ◽  
Single Boundary ◽  
Small Eigenvalues

We study the properties of single boundary spike solutions for the following singularly perturbed problem It is known that at a non-degenerate critical point of the mean curvature function H(P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N − 1) small eigenvalues. We obtain the exact asymptotics of the small eigenvalues in terms of H(P).

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