Results 31 to 40 of about 1,115 (71)

Estimates of the Laplacian Spectrum and Bounds of Topological Invariants for Riemannian Manifolds with Boundary

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
We set out to obtain estimates of the Laplacian Spectrum of Riemannian manifolds with non-empty boundary. This was achieved using standard doubled manifold techniques. In simple terms, we pasted two copies of the same manifold along their common boundary
Sabatini Luca
doaj   +1 more source

Lieb-Thirring inequalities with improved constants

, 2007
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi ...
Dolbeault, Jean, Laptev, Ari, Loss, Michael   +2 more
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An eigenvalue estimate for self-shrinkers in a Ricci shrinker

Advanced Nonlinear Studies
In this paper, we study the drifted Laplacian Δf on a hypersurface M in a Ricci shrinker (M̄,g,f) $\left(\bar{M},g,f\right)$ . We prove that the spectrum of Δf is discrete for immersed hypersurfaces with bounded weighted mean curvature in a Ricci ...
Conrado Franciele, Zhou Detang
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Monotonicity, continuity and differentiability results for the $L^p$ Hardy constant

, 2015
We consider the $L^p$ Hardy inequality involving the distance to the boundary for a domain in the $n$-dimensional Euclidean space. We study the dependence on $p$ of the corresponding best constant and we prove monotonicity, continuity and ...
Barbatis, Gerassimos, Lamberti, Pier Domenico   +1 more
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Characters and transfer maps via categorified traces

Forum of Mathematics, Sigma
We develop a theory of generalized characters of local systems in $\infty $ -categories, which extends classical character theory for group representations and, in particular, the induced character formula.
Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi, Lior Yanovski   +3 more
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An estimate for the number of bound states of the Schrödinger operator in two dimensions [PDF]

, 2004
For the Schrödinger operator -Δ + V on R^2 be the number of bound states. One obtains the following estimate: N(V) ≤ 1 + ∫_(R^2)∫_(R^2)|V(x)|V(y)|C_(1)ln|x-y|+C_2|^2 dx dy where C_1 = -1/2π and C_2 = (ln2-γ)/2π (γ is the Euler constant).
Stoiciu, Mihai
core  

Estimates on the first two buckling eigenvalues on spherical domains

, 2009
In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].Comment: This ...
Ashbaugh, Chen, Cheng, Guangyue Huang, Hile, Payne, Wang, Xingxiao Li, Xuerong Qi   +8 more
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Bounds for the sum of the first k-eigenvalues of Dirichlet problem with logarithmic order of Klein-Gordon operators

Advances in Nonlinear Analysis
We provide bounds for the sequence of eigenvalues {λi(Ω)}i{\left\{{\lambda }_{i}\left(\Omega )\right\}}_{i} of the Dirichlet problem (I−Δ)lnu=λuinΩ,u=0inRN\Ω,{\left(I-\Delta )}^{\mathrm{ln}}u=\lambda u\hspace{1em}{\rm{in}}\hspace{0.33em}\Omega ,\hspace{1.
Chen Huyuan, Cheng Li
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Bounds for eigenvalue ratios of the Laplacian [PDF]

, 2011
For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian.
Q. -m. Cheng, Qing-ming Cheng, X. Qi, Xuerong Qi   +3 more
core  

Minimizing Schrödinger eigenvalues for confining potentials

Advanced Nonlinear Studies
We consider the problem of minimizing the lowest eigenvalue of the Schrödinger operator −Δ + V in L2(Rd) ${L}^{2}({\mathbb{R}}^{d})$ when the integral ∫e −tV  dx is given for some t > 0. We show that the eigenvalue is minimal for the harmonic oscillator
Frank Rupert L.
doaj   +1 more source