scholarly journals Exponential gaps in the length spectrum

2020 ◽  
Vol 16 (0) ◽  
pp. 207-223
Author(s):  
Emmanuel Schenck ◽  
Keyword(s):  
Length Spectrum

scholarly journals Marked length rigidity for Fuchsian buildings

2018 ◽  
Vol 39 (12) ◽  
pp. 3262-3291
Author(s):  
DAVID CONSTANTINE ◽  
JEAN-FRANÇOIS LAFONT
Keyword(s):  
Automorphism Group ◽  
Riemannian Metrics ◽  
Length Spectrum ◽  
Negatively Curved ◽  
Spectrum Function ◽  
Marked Length Spectrum

We consider finite $2$-complexes $X$ that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT($-1$) metrics on $X$, which are piecewise hyperbolic and satisfy a natural non-singularity condition at vertices, are marked length spectrum rigid within certain classes of negatively curved, piecewise Riemannian metrics on $X$. As a key step in our proof, we show that the marked length spectrum function for such metrics determines the volume of $X$.

Rigidity for non-compact surfaces of finite area and certain Kähler manifolds

1995 ◽  
Vol 15 (3) ◽  
pp. 475-516 ◽  
Author(s):  
Jianguo Cao
Keyword(s):  
Length Spectrum ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Finite Area ◽  
Marked Length Spectrum ◽  
Compact Surfaces

AbstractWe first consider the rigidity of the marked length spectrum for non-compact surfaces of finite area.

scholarly journals Non-backtracking cycles: length spectrum theory and graph mining applications

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Leo Torres ◽  
Pablo Suárez-Serrato ◽  
Tina Eliassi-Rad
Keyword(s):  
Graph Mining ◽  
Length Spectrum
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