Gaussian bounds of heat kernels for Schrödinger operators on Riemannian manifolds

2006 ◽  
Vol 39 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Masayoshi Takeda
Keyword(s):  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Heat Kernels ◽  
Schrodinger Operators ◽  
Gaussian Bounds

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

scholarly journals POSITIVE PERTURBATIONS OF SELF-ADJOINT SCHRÖDINGER OPERATORS ON RIEMANNIAN MANIFOLDS

2005 ◽  
Vol 02 (04) ◽  
pp. 543-552
Author(s):  
OGNJEN MILATOVIC
Keyword(s):  
Riemannian Manifold ◽  
Differential Expression ◽  
Riemannian Manifolds ◽  
Integrable Function ◽  
Schrödinger Operators ◽  
Sufficient Conditions ◽  
Schrodinger Operators ◽  
Square Integrable Function

We consider a Schrödinger differential expression L0 = ΔM + V0 on a Riemannian manifold (M,g) with metric g, where ΔM is the scalar Laplacian on M and V0 is a real-valued locally square integrable function on M. We consider a perturbation L0 + V, where V is a non-negative locally square-integrable function on M, and give sufficient conditions for L0 + V to be essentially self-adjoint on [Formula: see text]. This is an extension of a result of T. Kappeler.

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