3 citations · 6 across the 10 of their papers we have counts for
10 papers
Calabi-Yau structures on Rabinowitz Fukaya categories
Hanwool Bae, Wonbo Jeong, Jongmyeong Kim
In this paper, we prove that the derived Rabinowitz Fukaya category of a Liouville domain of dimension is -Calabi--Yau assuming the wrapped Fukaya category of a…
The fractional -Laplacian on hyperbolic spaces
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We present three equivalent definitions of the fractional -Laplacian , , , with normalizing constants, on hyperbolic spaces. The expli…
Cluster categories from Fukaya categories
Hanwool Bae, Wonbo Jeong, Jongmyeong Kim
We show that the derived wrapped Fukaya category , the derived compact Fukaya category and the cocore disks of th…
Categorical entropy, (co-)t-structures and ST-triples
Jongmyeong Kim
In this paper, we study a dynamical property of an exact endofunctor of a triangulated category . In particular, we are interested in…
On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity
Federico Barbacovi, Jongmyeong Kim
In topological dynamics, the Gromov--Yomdin theorem states that the topological entropy of a holomorphic automorphism of a smooth projective variety is equal to the logarithm o…
Harnack inequality for fractional Laplacian-type operators on hyperbolic spaces
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We establish the Krylov--Safonov theory for a large class of nonlocal operators of order on hyperbolic spaces with curvature . We prove the…
Entropy of the composition of two spherical twists
Federico Barbacovi, Jongmyeong Kim
Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of…
Computation of categorical entropy via spherical functors
Jongmyeong Kim
We study the relationship between the categorical entropy of the twist and cotwist functors along a spherical functor. In particular, we prove the categorical entropy of the twist…
Harnack inequality for Nonlocal operators on Manifolds with nonnegative curvature
Jongmyeong Kim, Minhyun Kim, Ki-Ahm Lee
We establish the Krylov Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sec…
Systolic inequalities, Ginzburg dg algebras and Milnor fibers
Jongmyeong Kim
We prove categorical systolic inequalities for the derived categories of 2-Calabi--Yau Ginzburg dg algebras associated to ADE quivers and explore their symplecto-geometric aspects.