Commensurators of geometrically rigid residually finite hyperbolic groups have bounded average distortion.
L_2 - C ohomology of pseudoconvex domains with complete K \"ahler metric
8 Pith papers cite this work. Polarity classification is still indexing.
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Branched covers of hyperbolic groups along quasiconvex subgroups are defined and realized through deep Dehn fillings, generalizing 3-manifold constructions and potentially producing spherical-boundary examples.
Under the Strong Atiyah Conjecture and vanishing b1^(2), L2-Betti numbers of character kernels define a polytope-induced Thurston seminorm on H^1(G;R), with combinatorial splitting-complexity interpretations for free-by-cyclic and admissible 3-manifold groups.
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
The Fefferman-Szegő metric on C^∞-smooth bounded strongly pseudoconvex domains in C^n has vanishing L2-Dolbeault cohomology outside middle degree, C^∞ bounded geometry, and yields rigidity results implying the domain is biholomorphic to the ball under gradient Kahler-Ricci soliton or constant scalar
Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.
Establishes lower bound for Kähler hyperbolicity modulus on complete Kähler manifolds via boundary gradient length of plurisubharmonic functions, with applications to symmetric and strongly pseudoconvex domains.
Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.
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The Invariant Szeg\H{o} metric on strongly pseudoconvex domains
The Fefferman-Szegő metric on C^∞-smooth bounded strongly pseudoconvex domains in C^n has vanishing L2-Dolbeault cohomology outside middle degree, C^∞ bounded geometry, and yields rigidity results implying the domain is biholomorphic to the ball under gradient Kahler-Ricci soliton or constant scalar
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The invariant Szeg\H{o} metric on Egg domains
Explicit Fefferman-Szegő metric on egg domains D_{2m} is Kähler-Einstein and proportional to Bergman metric iff m=1.
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K\"ahler Hyperbolicity Modulus for Simply-connected K\"ahler Hyperbolic manifolds
Establishes lower bound for Kähler hyperbolicity modulus on complete Kähler manifolds via boundary gradient length of plurisubharmonic functions, with applications to symmetric and strongly pseudoconvex domains.