15 citations · 93 across the 26 of their papers we have counts for
28 papers
Mirror functor for deformed preprojective algebras
Hansol Hong, Siu-Cheong Lau, Ju Tan
We study localized homological mirror symmetry associated to an immersed Lagrangian brane , possibly equipped with a higher rank flat bundle, of a symplectic manifold $…
Asymptotic Plateau problem via equidistant hyperplanes
Han Hong, Haizhong Li, Meng Zhang
We show the existence of a complete, strictly locally convex hypersurface within that adheres to a curvature equation applicable to a broad range of curvature fu…
Large Steklov eigenvalues on hyperbolic surfaces
Xiaolong Hans Han, Yuxin He, Han Hong
In this paper, we first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue tends to infinity…
Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Sam Bardwell-Evans, Man-Wai Mandy Cheung, Hansol Hong +1
We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagra…
Capillary surfaces: stability, index and curvature estimates
Han Hong, Artur B. Saturnino
In this paper we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immerse…
Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology
Nicolau S. Aiex, Han Hong
We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the graphical sense away from a finite set o…
Maurer-Cartan deformation of Lagrangians
Hansol Hong
The Maurer-Cartan algebra of a Lagrangian is the algebra that encodes the deformation of the Floer complex as an -algebra. We identify the Maurer-Cartan a…
Higher dimensional surgery and Steklov eigenvalues
Han Hong
We show that for compact Riemannian manifolds of dimension at least with nonempty boundary, we can modify the manifold by performing surgeries of codimension or higher, whi…
Big Quantum cohomology of orbifold spheres
Lino Amorim, Cheol-Hyun Cho, Hansol Hong +1
We construct a Kodaira-Spencer map from the big quantum cohomology of a sphere with three orbifold points to the Jacobian ring of the mirror Landau-Ginzburg potential function. Thi…
-equivariant disc potentials for toric Calabi-Yau manifolds
Hansol Hong, Yoosik Kim, Siu-Cheong Lau +1
We study the equivariant disc potentials for immersed SYZ fibers in toric Calabi-Yau manifolds. The immersed Lagrangians play a crucial role in the partial compactification of the…
Index Estimates for Surfaces with Constant Mean Curvature in -dimensional Manifolds
Nicolau S. Aiex, Han Hong
We prove index estimates for closed and free boundary CMC surfaces in certain -dimensional submanifolds of some Euclidean space. When the mean curvature is large enough we are a…
Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period
Hansol Hong, Yu-Shen Lin, Jingyu Zhao
We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for…
Gluing Localized Mirror Functors
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry an…
Immersed two-spheres and SYZ with Application to Grassmannians
Hansol Hong, Yoosik Kim, Siu-Cheong Lau
We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sp…
Moduli of Lagrangian immersions with formal deformations
Hansol Hong, Siu-Cheong Lau
We introduce a joint project with Cheol-Hyun Cho on the construction of quantum-corrected moduli of Lagrangian immersions. The construction has important applications to mirror sym…
Mirror of Atiyah flop in symplectic geometry and stability conditions
Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau +1
We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct…
Sharp geometric inequalities for the general -affine capacity
Han Hong, Deping Ye
In this article, we propose the notion of the general -affine capacity and prove some basic properties for the general -affine capacity, such as affine invariance and monoton…
The -capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems
Han Hong, Deping Ye, Ning Zhang
In this paper, combining the -capacity for with the Orlicz addition of convex domains, we develop the -capacitary Orlicz-Brunn-Minkowski theory. In particular,…
The Orlicz-Petty bodies
Baocheng Zhu, Han Hong, Deping Ye
This paper is dedicated to the Orlicz-Petty bodies. We first propose the homogeneous Orlicz affine and geominimal surface areas, and establish their basic properties such as homoge…
Counting of Holomorphic Orbi-spheres in and Determinant Equation
Hansol Hong, Hyung-Seok Shin
We count the number of holomorphic orbi-spheres in the -quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic…
Noncommutative homological mirror functor
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
We formulate a constructive theory of noncommutative Landau-Ginzburg models mirror to symplectic manifolds based on Lagrangian Floer theory. The construction comes with a natural f…
On quantum cohomology ring of elliptic orbifolds
Hansol Hong, Hyung-Seok Shin
We compute quantum cohomology ring of elliptic orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-cur…
Localized mirror functor constructed from a Lagrangian torus
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A-infinity funct…
Lagrangian Floer potential of orbifold spheres
Cheol-Hyun Cho, Hansol Hong, Sang-hyun Kim +1
For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and…