• Differential Geometry
• Geometric Analysis

-Fixed point and rigidity theorems for harmonic maps from simplicial complexes to NPC spaces with G. Daskalopoulos. preprint
-Free boundary regularity of the Singular Plateau Problem with S. Yamada. preprint
-Harmonic maps from a Riemannian polyhedron. preprint
-Harmonic maps from simplicial complexes and geometric rigidity with G. Daskalopoulos.  To appear in Journal of Differential Geometry.
-Harmonic maps from two-complexes with G. Daskalopoulos.  Communications in Analysis and Geometry 14 (2006) 497-549.
-The parameterized Steiner problem and the singular Plateau Problem via energy with S. Yamada.  Transactions of the American Mathematical Society 358 (2006) 2875-2895. 
-Harmonic maps and minimal surfaces in singular geometry. Clay Mathematics Proceedings 2 (2005) 773-782.
-Regularity of Harmonic maps from a flat complex. Variational Problems in Riemannian Geometry:  Bubbles, Scans and Geometric Flows.  Progress in Non-Linear Differential Equations.  Editor:  P. Baird et. al.
-A variational construction of the Teichmuller map. Calculus of Variations 21 (2004) 15-46.
-Uniqueness theorems for harmonic maps into metric spaces. Communications in Contemporary Mathematics 4 (2002) 725-750.
-Harmonic maps into spaces with an upper curvature bound in the sense of Alexandrov. Math. Z. 242 (2002) 633-661.
-Harmonic maps between surfaces and Teichmuller spaces. American Journal of Mathematics 124 (2002) 451-481.
-Curvature of minimal surfaces in singular spaces. Communications in Analysis and Geometry 9 (2001) 3-34.
-The Bernstein problem for complete Lagrangian stationary surfaces. Proceedings of the American Mathematical Society. 129 (2000) 573-580.
-Some properties of minimal surfaces in singular spaces. Transactions of the American Mathematical Society 352 (2000) 3957-3969.
-Structure of singular spaces of dimension 2. Manuscripta Mathematica 100 (1999) 375-389.
-Minimal surfaces and conformal mappings into singular spaces. Thesis at Stanford University.

                 Syllabus

                 Homework

                Solution Set for Exam 1

                Solution Set for Exam 2

                 Syllabus

                 Homework

                 Syllabus

                 Homework Assignments

                 Sample Midterm #1

                 Sample Midterm #1 Solutions

                 Sample Midterm #2

                 Sample Midterm #2 Solutions

                 Midterm Solutions

                 Sample Final #1 Solutions

                 Sample Final #2

                 Sample Final #2 Solutions

                 Syllabus

                 Homework Assignments

                 Homework Solutions

                 Supplemental Material for Exam 1

                 Solutions to Exam 1

                 Supplemental Material for Exam 2

                 Solutions to Exam 2

                 Supplemental Material for Final Exam

                 Syllabus

                 Homework Assignments

                 Syllabus

                 Homework Assignments