Finiteness theorem for multi-K-bi-Lipschitz equivalence of map germs

2018 ◽  
Vol 291 (16) ◽  
pp. 2381-2387
Author(s):  
Lev Birbrair ◽  
João Carlos Ferreira Costa ◽  
Edvalter Da Silva Sena Filho ◽  
Rodrigo Mendes
Keyword(s):  
Finiteness Theorem ◽  
Lipschitz Equivalence

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 Determinantal variety and normal embedding

2017 ◽  
Vol 10 (01) ◽  
pp. 27-34 ◽  
Author(s):  
K. Katz ◽  
M. Katz ◽  
D. Kerner ◽  
Y. Liokumovich
Keyword(s):  
Metric Space ◽  
Space Structure ◽  
The Other ◽  
Intrinsic Metric ◽  
Lipschitz Equivalence ◽  
Other Hand ◽  
Determinantal Variety ◽  
Conical Structure ◽  
Positive Determinant

The space [Formula: see text] of matrices of positive determinant inherits an extrinsic metric space structure from [Formula: see text]. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in [Formula: see text] gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on [Formula: see text], exploiting the conical structure of the stratification of the space of [Formula: see text] matrices by rank.

scholarly journals Lipschitz equivalence of self-similar sets and hyperbolic boundaries II

2015 ◽  
Vol 2 (1) ◽  
pp. 53-79 ◽  
Author(s):  
Guo-Tai Deng ◽  
Ka-Sing Lau ◽  
Jun Luo
Keyword(s):  
Lipschitz Equivalence ◽  
Self Similar
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