A finiteness theorem for open semi-algebraic sets, with applications to Hilbert’s 17th problem

1982 ◽  
pp. 79-97 ◽  
Author(s):  
Charles N. Delzell
Keyword(s):  
Finiteness Theorem ◽  
Algebraic Sets ◽  
17Th Problem

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.

Affine algebraic sets relative to an algebraic theory

1999 ◽  
Vol 65 (1-2) ◽  
pp. 54-76 ◽  
Author(s):  
Yves Diers
Keyword(s):  
Algebraic Theory ◽  
Algebraic Sets

Points near real algebraic sets

2014 ◽  
Vol 142 (12) ◽  
pp. 4127-4132
Author(s):  
W. M. Schmidt ◽  
U. Zannier
Keyword(s):  
Algebraic Sets
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