scholarly journals The cohomological equation and invariant distributions for horocycle maps

2012 ◽  
Vol 34 (1) ◽  
pp. 299-340 ◽  
Author(s):  
JAMES TANIS
Keyword(s):  
Compact Manifolds ◽  
Invariant Distributions ◽  
Cohomological Equation ◽  
Sobolev Estimates

AbstractWe study the invariant distributions for horocycle maps on $\Gamma \backslash SL(2, \mathbb {R})$and prove Sobolev estimates for the cohomological equation of horocycle maps. As an application, we obtain a rate of equidistribution for horocycle maps on compact manifolds.

scholarly journals Uniform Sobolev estimates on compact manifolds involving singular potentials

2021 ◽  
Author(s):  
Matthew Blair ◽  
Xiaoqi Huang ◽  
Yannick Sire ◽  
Christopher Sogge
Keyword(s):  
Compact Manifolds ◽  
Singular Potentials ◽  
Sobolev Estimates

Sobolev Estimates for the Wave Operator on compact Manifolds

1992 ◽  
Vol 17 (11-12) ◽  
pp. 1867-1887 ◽  
Author(s):  
D. Jerison ◽  
C.D. Sogge ◽  
Z. Zhou
Keyword(s):  
Wave Operator ◽  
Compact Manifolds ◽  
Sobolev Estimates
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