#HyperbolicGeometry
October 31, 2025 at 1:04 AM
March 30, 2026 at 9:18 PM
Poincaré disk — {4,5} hyperbolic tessellation. 5 squares meeting at each vertex: impossible in Euclidean geometry, valid in hyperbolic. All tiles equal size — they only appear to shrink toward the infinite boundary. #MathArt #HyperbolicGeometry
February 26, 2026 at 3:27 AM
Extending the foundational Lieb-Schultz-Mattis theorem to hyperbolic (negatively curved) geometries: fractional fillings on non-Euclidean lattices enforce ground-state degeneracy, with implications for realizing exotic quantum phases like spin liquids.

#QuantumTheory #HyperbolicGeometry #Research
Lieb-Schultz-Mattis Constraints for Hyperbolic Lattices
arxiv.org
May 18, 2026 at 4:49 AM
Shin-Ichi Ohta studies discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces, extending results on nonpositively curved spaces and semi-contractions.

🔗 doi.org/10.1142/S021...

#Mathematics #Geometry #ConvexAnalysis #HyperbolicGeometry #GradientFlows
May 7, 2026 at 1:14 AM