Kang-Hyurk Lee

Professor

Department of Mathematics, Gyeongsang National University

Address: 501, Jinju-daero, Jinju-si, Gyeongsangnam-do, 52828

Office: 419, Bldg# 354

email: nyawoo(at)gnu(dot)ac(dot)kr, nyawoo(at)gmail(dot)com

Research

Research fields: Several Complex Variables, Complex Geometry

Research interests: holomorphic automorphism groups, negatively curved Kähler manifolds, the rescaling method

Publications

• A characterization of the unit ball by a Kähler-Einstein potential (with Choi, Young-Jun & Seo, Aeryeong), J. Geom. Anal. 33 (2023), Paper No 133, 18pp. (Journal link, arXiv:2209.13830)

• The method of potential rescaling: overview and the localization (with Choi, Young-Jun). Complex Anal. Synerg. 9 (2023), no. 1, Paper No. 6, 10 pp.

• Homogeneous almost complex manifolds and their compact quotients (with Kim, Kang-Tae & Nagata, Yoshikazu), Internat. J. Math. 32 (2021), no. 6, Paper No. 2150034, 8 pp. 

• Existence of a complete holomorphic vector field via the Kähler-Einstein metric (with Choi, Young-Jun), Ann. Global Anal. Geom. 60 (2021), no. 1, 97–109.

• A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group, J. Math. Anal. Appl. 499 (2021), no. 1, Paper No. 124997, 15 pp. 

• A certain Kähler potential of the Poincaré metric and its characterization (with Y.-J. Choi, S. Yoo),  J. Korean Math. Soc. 57 (2020), no. 6, 1335–1345.

• Pseudo-Hermitian manifolds with automorphism group of maximal dimension (with J.-C. Joo), Tohoku Math. J. (2) 70 (2018), no. 4, 487–510. 

• Characterizations of strongly pseudoconvex models in almost complex and CR geometries, Complex analysis and geometry, 221–233, Springer Proc. Math. Stat., 144, Springer, Tokyo, 2015. 

• Subconformal Yamabe equation and automorphism groups of almost CR manifolds (with J.-C. Joo),  J. Geom. Anal. 25 (2015), no. 1, 436–470. 

• On the upper-semicontinuity of automorphism groups of model domains in almost complex manifolds (with J. Byun, S. Lee), J. Math. Anal. Appl. 421 (2015), no. 1, 118–130. 30F35

• Domains with a contracting automorphism at a boundary point (with J. Byun), Michigan Math. J. 63 (2014), no. 1, 19–25. 

• Complete prolongation for infinitesimal automorphisms on almost complex manifolds (with H. Kim), Math. Z. 264 (2010), no. 4, 913–925. 

• Integrable submanifolds in almost complex manifold (with C.-K. Han), J. Geom. Anal. 20 (2010), no. 1, 177–192. 

• On the automorphism group of strongly pseudoconvex domains in almost complex manifolds (with J. Byun, H. Gaussier), Ann. Inst. Fourier (Grenoble) 59 (2009), no. 1, 291–310.

• Strongly pseudoconvex homogeneous domains in almost complex manifolds, J. Reine Angew. Math. 623 (2008), 123–160. 

• Domains in almost complex manifolds with an automorphism orbit accumulating at a strongly pseudoconvex boundary point, Michigan Math. J. 54 (2006), no. 1, 179–205. 

• Almost complex manifolds and Cartan's uniqueness theorem, Trans. Amer. Math. Soc. 358 (2006), no. 5, 2057–2069.

Preprints

• Almost CR manifolds with contracting CR automorphism (with Joo, Jae-Cheon), submitted

• A Kähler potential on the unit ball with constant differential norm  (with Seo, Aeryeong), submitted (arXiv:2303.10012)