7 papers
A Tutorial on Bregman Projection in Statistics
Gunhee Cho, Jae Kwang Kim, Yumou Qiu
A single geometric operation -- projecting a reference onto a constrained family under a Bregman divergence -- underlies a striking range of statistical methods. This tutorial deve…
Complex Analysis and Riemann Surfaces: A Graduate Path to Algebraic Geometry
Gunhee Cho, Bae Dongsong, Junhyuk Boo +8
This book develops a computation-driven route from classical complex analysis to compact Riemann surfaces and algebraic geometry. It begins with holomorphic and meromorphic functio…
Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds
Gunhee Cho, Myungsin Cho
We prove that the Green--Griffiths--Demailly (GGD) hyperbolicity thresholds are structurally invariant. In other words, the minimal jet order and asymptotic growth rate at which in…
Deterministic--Distance Couplings of Brownian Motions on Radially Isoparametric Manifolds
Gunhee Cho, Hyun Chul Jang, Taeik Kim
We develop a unified geometric framework for coadapted Brownian couplings on radially isoparametric manifolds (RIM)--spaces whose geodesic spheres have principal curvatures $κ_1(r)…
Support-Projected Petz Monotone Geometry of Pure Two-Qubit Families: Universal Three-Channel Decomposition and Non-Reduction of Curvature Invariants
Gunhee Cho, Jeongwoo Jae
We develop a support-projected Petz monotone geometry for pure two-qubit families, obtained by pulling back arbitrary Petz monotone quantum metrics to circuit-defined submanifolds…
Hyperbolic Embeddings in Toric Geometry: Effectivity and Deformation Stability
Jaewon Yoo, Gunhee Cho
We study the deformation behavior of Kobayashi hyperbolic embeddings for complements of divisors in projective toric varieties. In the toric setting, entire curves in divisor compl…
Equivalence of Invariant metrics via Bergman kernel on complete noncompact Kähler manifolds
Gunhee Cho, Kyu-Hwan Lee
We study equivalence of invariant metrics on noncompact Kähler manifolds with a complete Bergman metric of bounded curvature. Especially only the boundedness of the ratio between B…