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Work Experience

• Associate Research Fellow Institute of Mathematics, Academia Sinica 1999 - Present
• Assistant Research Fellow Institute of Mathematics, Academia Sinica 1994 - 1999
• Associate Professor Institute of Applied Mathematics, National Tsing Hua University 1987 - 1993

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Research Descriptions

Dr. Liang's major research interests are variational problem, geometric analysis and problems of partial differential equations related to minimal surfaces or surfaces of constant mean curvature.

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Selected Publications

1. "Hypersurfaces of constant curvature in hyperbolic space" , Journal of Progressive Research in Mathematics , 13 (3), 2237-2244, 2018-05.
2. "On hypersurfaces of constant Gauss curvature with prescribed boundary" , Theoretical mathematics and applications , 6 (2), 37-49, 2016.
3. "Delaunay-like surfaces in S^n+1" , Studies in Mathematical Sciences , 2 (2), 2011-05.
4. "Interior gradient estimates for solutions to the mean curvature equation" , International Math. Forum , 3 (9), 407-448, 2008.
5. "Second derivative estimates for solutions to the mean curvature equation" , Internatuinal Math. Forum , 3 (29), 1414-1435, 2008.
6. "Gauss curvature estimates for surfaces whose mean curvature is constant or has special properties" , International Math. Forum , 2 (53), 2607-2643, 2007.
7. "Isoperimetric inequalities, the torsion problem, and the first eigenvalue of Laplacian of multiply-connected, compact surfaces with boundary" , International Mathematical Forum , 2 (17), 835-872, 2007.
8. "Boundary regularity for capillary surfaces" , Georgian Math. J , 12, 283-307, 2005.
9. "Boundary behavior of capillary surfaces possibly with extremal boundary angles" , Internal. J. Math. Math. Soc , 2005 (24), 3925-3950, 2005.
10. "Global boundedness, interior gradient estimates and boundary regularity for the mean curvature equation with boundary conditions" , Interl J. Math. Math. Soc. , 18, 913-948, 2004.
11. "Harnack's inequalities for solutions to the mean curvature equation and to the capillarity problem" , Rend.Sem. Mat. Univ. Padova,110, 2003 , 110, 57-96, 2003.
12. "Interior Holder estimates for nonparametric surfaces of prescribed mean curvature" , Proc. Royal Soc. of Edingburgh , 133A, 625-638, 2003.
13. (with Chun-Chung Hsieh and Jenn-fang Hwang) "Phagemen-Lindelof theorem for minimal surfaces in higher dimensions" , Pacific J. of Math. , 207 (1), 183-198, 2002.
14. "Absolute gradient bounds for nonparametric hypersurfaces of constant mean curvature" , Ann.Univ.Ferrara-Sez. VII-Sc.Mat. , XLVIII, 189-217, 2002.
15. "Level sets of Gauss curvature in surfaces of constant mean curvature" , Rend. Sem. Mat. Univ. Padova , 104, 1-26, 2000.
16. "On the minimum number of components divided by level set through a critical point of the subtraction of two solutions of the equation of prescribed mean curvature" , Analysis , 19, 117-142, 1999.
17. "Absolute gradient bounds for nonparametric hypersurfaces of constant mean curvature and the structure of generalized solutions of the constant mean curvature equation" , Calc. Var. and P.D.E's , 7, 99-123, 1998.
18. "Moon hypersurfaces and some related existence results of capillary hypersurfaces without gravity and of rotational symmetry" , Pacific J. of Math. , 172 (3), 433-460, 1996.
19. "An absolute gradient bound for nonparametric surfaces of constant mean curvature" , Indiana Univ. Math. J. , 41 (3), 569-604, 1992.