Associate Research Fellow |   Liang, Fei-tsen
Contact Information
• liang$\color{red}{@}$math.sinica.edu.tw
• +886 2 2368-5999 ext. 706
• +886 2 2368-9771
Research Interests
• Partial Differential Equations
Education
• Ph.D. in Mathematics Stanford University (1982-1987)
• B.S. in Mathematics National Taiwan University (1978-1982)

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

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.

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.