Research

Publications/Preprints

-Notes on Harmonic Maps, With G. Daskalopoulos

-Infinite energy harmonic maps and rigidity, With G. Daskalopoulos. Submitted for publication.

-Infinite energy harmonic maps from Riemann surface to CAT(0) spaces. Submitted for publication.

-Infinite energy harmonic maps from Kahler surfaces to CAT(0) spaces. With G.~Daskalopoulos. Accepted for publication in Advanced Nonlinear Studies.

-Uniqueness of equivariant harmonic maps to symmetric spaces and buildings, with G. Daskalopoulos. Accepted for publication in Mathematical Research Letters

-On the singular set of nonlinear degenerate PDE arising in Teichmuller theory, with G. Daskalopoulos. Proceedings of the American Mathematical Society 150 (2022) 411-422.

-Harmonic branched covering and uniformization of CAT(k) spheres, with C. Breiner. Journal für die reine und angewandte Mathematik (Crelles Journal) 779 (2021) 123-166.

-Rigidity of Teichmüller space, with G. Daskalopoulos. Inventiones Mathematicae 224 (2021) 791-916.

-Existence of harmonic maps into CAT(1) spaces, with C. Breiner, A. Fraser, L. Huang, P. Sargent, Y. Zhang. Communications in Analysis and Geometry 28 (2020) 781-835.

- Essential Regularity of the Model Space for the Weil-Petersson Metric, with G. Daskalopoulos. Journal für die reine und angewandte Mathematik (Crelles Journal) 750 (2019) 53-96.

- Surfaces groups acting on CAT(-1) spaces, with G. Daskalopoulos, A. Sanders and A. Vdovina Alina. Ergodic Theory and Dynamical Systems 39, 1843-8564 (2019).

- Regularity of harmonic maps from Polyhedra to CAT(1) Spaces, with C. Breiner, A. Fraser, L. Huang, P. Sargent, and Y. Zhang. Calculus of Variation and Partial Differential Equations 57 (2018) 781-835.

- Higgs bundles over cell complexes and representations of finitely presented groups, with G. Daskalopoulos and G. Wilkin, Graeme. Pacific Journal of Mathematics 296 (2018), 31-55.

-C1-estimates for the Weil-Petersson metric, with G. Daskalopoulos. Transactions of the American Mathematical Society 369 (2017), 2917-2950

- On the Singular Set of Harmonic Maps into DM-Complexes with G. Daskalopoulos. Memoir of the American Mathematical Society 239 (2016).

- On the Intrinsic Differentiability Theorem of Gromov-Schoen with G. Daskalopoulos. Surveys in Geometric Analysis and Relativity ALM 20, 189-203.

- Monotonicity properties of harmonic maps into NPC spaces with G. Daskalopoulos. Journal of Fixed Point Theory and Applications 11 (2012) 225-243.

- Superrigidity of Hyperbolic Buildings with G. Daskalopoulos and Alina Vdovina, Geometric and Functional Analysis 21 (2011) 905-919.

-The Plateau problem in Alexandrov Spaces with P. Zulkowski. Journal of Differential Geometry 85 (2010), no. 2, 315-356.

- Local uniformization and free boundary regularity of minimal singular surfaces with S. Yamada, Journal of Geometric Analysis 21 (2011) 743–766.

- Harmonic maps between singular spaces Iwith G. Daskalopoulos. Comm. Anal. Geom. 18 (2010) no. 2, 257-337.

-Fixed point and rigidity theorems for harmonic maps from simplicial complexes to NPC spaces with G. Daskalopoulos. Geometriae Dedicata 141 (2009), 33-57.

-Harmonic maps from simplicial complexes and geometric rigidity with G. Daskalopoulos. J. Differential Geom. 78 (2008), no. 2, 269-293.

-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.