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Creators/Authors contains: "CONSTANTINE, DAVID"

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  1. ; ; ; ; (, International Mathematics Research Notices)
    Abstract Consider a compact surface of genus $$\geq 2$$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $$2\pi $$. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson, we prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not support the full pressure. Moreover, we show that the pressure gap holds for any potential that is locally constant on a neighborhood of the singular set. Finally, we establish that the corresponding equilibrium states have the $$K$$-property and closed regular geodesics equidistribute. 
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  2. ; (, Ergodic Theory and Dynamical Systems)
    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 $$X$$ . 
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  3. ; ; (, Groups, Geometry, and Dynamics)
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  4. ; ; (, Journal de l’École polytechnique — Mathématiques)
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