Four counterexamples to converses of geometric-finiteness implications in round convex projective geometry are constructed using 4-dimensional domains invariant under the irreducible representation of SL₂(ℝ).
Duke Math
3 Pith papers cite this work, alongside 41 external citations. Polarity classification is still indexing.
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The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.
Defines Kobayashi-type pseudometric on domains in real-type Nagano spaces; proves it is a metric iff domain avoids photon minus point, and is never Gromov hyperbolic in higher rank for strongly R-proper dually convex divisible domains.
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On 4-dimensional convex projective domains invariant by a lattice of $\mathrm{SL}_2 (\mathbb{R})$
Four counterexamples to converses of geometric-finiteness implications in round convex projective geometry are constructed using 4-dimensional domains invariant under the irreducible representation of SL₂(ℝ).
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An Affine Invariant Minkowski Problem
The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.
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Metric properties of domains in real-type Nagano spaces
Defines Kobayashi-type pseudometric on domains in real-type Nagano spaces; proves it is a metric iff domain avoids photon minus point, and is never Gromov hyperbolic in higher rank for strongly R-proper dually convex divisible domains.