Every cusp-like end of a finite-type constant-curvature surface in hyperbolic space carries a well-defined Steiner point, and a new Schläfli formula ties these points to variations of generalized volume and renormalized energy.
M., A cyclic extension of the earthquake flow I, Geom
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On the asymptotic geometry of finite-type $k$-surfaces in three-dimensional hyperbolic space
Every cusp-like end of a finite-type constant-curvature surface in hyperbolic space carries a well-defined Steiner point, and a new Schläfli formula ties these points to variations of generalized volume and renormalized energy.