Lee, Woon Yin (Paul)


Address:     Room 216, Lady Shaw Building, the Chinese University of Hong Kong, Shatin, Hong Kong

Phone:        (852) 3943-7978

Email:         paulwylee@@gmail.com


l   Fall 2016: MATH1030 A & B Linear Algebra I

l   Spring 2015: MATH1030 C & D Linear Algebra I

l   Spring 2015: MATH5012 Real Analysis II

l   Spring 2015: GENA1113 Student-oriented Teaching and Seminar

l   Spring 2014: MATH1030 C & D Linear Algebra I

l   Spring 2014: MATH2010 E Advanced Calculus I

l   Spring 2013: MATH1030 C Linear Algebra I

l   Fall 2012: MATH2010 A & B Advanced Calculus I

l   Spring 2012: MATH3423 Hyperbolic Geometry

l   Spring 2012: MATH6081 Introduction to Optimal Transportation

l   Fall 2011: MATH2010B Advanced Calculus I


1.      Poisson geometry and first integrals of geostrophic equations, with Boris Khesin, Physica D, vol.237 (2008), 2072-2077.

2.      Optimal transportation under nonholonomic constraints, with Andrei Agrachev, Trans. Amer. Math. Soc. 361 (2009), 6019-6047.

3.      A nonholonomic Moser theorem and optimal mass transport, with Boris Khesin, J. Symplectic Geom. 7 (2009), no.4, 381-414.

4.      Continuity of optimal control costs and its application to weak KAM theory, with Andrei Agrachev, Calc. Var. Partial Differential Equations 39 (2010), no. 1-2, 213-232.

5.      The Ma-Trudinger-Wang curvature for natural mechanical actions, with Robert J. McCann, Calc. Var. Partial Differential Equations 41 (2010), no. 1-2, 285-299.

6.      New computable necessary conditions for the regularity theory of optimal transportation, SIAM J. Math. Anal., 42 (2010), no.6, 3054-3075.

7.      A remark on the potentials of optimal transport maps, Acta. Appl. Math., 115 (2011), no.2, 123-138.

8.      New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions, with Jiayong Li, SIAM J. Math. Anal., 44 (2012), 61-73.

9.      On surfaces in three dimensional contact manifolds, Canad. J. Math., 65 (2013), no. 3, 621-633.

10.  Displacement interpolations from a Hamiltonian point of view. J. Funct. Anal. 265 (2013), no. 12, 3163-3203.

11.  Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds, with Andrei Agrachev, Math. Ann. 360 (2014), no. 1-2, 209-253.

12.   Bishop and Laplacian comparison theorems on three dimensional contact subriemannian manifolds with symmetry, with Andrei Agrachev, J. Geom. Anal. 25 (2015), no. 1,


13.  On the Jordan-Kinderlehrer-Otto scheme, J. Math. Anal. Appl. 429 (2015) no. 1, 131-142.

14.  Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds, with Chengbo Li and Igor Zelenko, Discrete Contin. Dyn. Syst. Series A (2016),

no. 1, 303-321.

15.  On measure contraction property without Ricci curvature lower bound, (2014), 18 pp, to appear in Potential Analysis.

16.  Generalized Li-Yau estimates and Huisken's monotonicity formula, arXiv: 1211.5559 (2013), 25pp, submitted for publication.

17.  Differential Harnack inequalities for a family of sub-elliptic diffusion equations on Sasakian manifolds, arXiv: 1302.3315 (2013), 27pp, submitted for publication.

18.  Bishop and Laplacian comparison theorems on Sasakian manifolds, with Chengbo Li, arXiv: 1310.5322 (2013), 38pp, submitted for publication.

19.  Differential Harnack inequalities for linear parabolic equations, arXiv: 1505.06465 (2015), 15pp, submitted for publication.

20.  The Harnack inequality and the Jordan-Kinderlehrer-Otto scheme, arXiv: 1509.01894 (2015), 9pp, submitted for publication.

21.  Sharp Harnack inequalities for a family of hypoelliptic diffusions, arXiv: 1510.07537 (2015), 16pp, submitted for publication. 

22.  Ricci curvature lower bounds on Sasakian manifolds, arXiv: 1511.09381 (2015), 16pp, preprint.


23.  Matrix Factorizations via the Inverse Function Theorem, arXiv: 1408.2611 (2014), 6 pp.