Research

PUBLICATIONS AND PREPRINTS:

Daskalopoulos, Georgios; Uhlenbeck, Karen; Analytic properties of  Stretch maps and geodesic laminations. Submitted (arXiv:2205.08250).

Daskalopoulos, Georgios; Uhlenbeck, Karen; Transverse Measures and Best Lipschitz and Least Gradient Maps. to Appear J. of Diff. Geom (arXiv:2010.06551).

Brotbek, Damian; Daskalopoulos, Georgios; Ya, Deng; Mese, Chikako. Representations of fundamental groups and logarithmic symmetric differential forms. Submitted. (arXiv:2206.11835).

Daskalopoulos, Georgios; Mese, Chikako. Infinite energy harmonic maps from Kaehler surfaces to CAT(0) spaces. To appear Advanced Nonlinear Studies.

Daskalopoulos, Georgios; Mese, Chikako. Infinite energy harmonic maps from Riemann surface to CAT(0) spaces. To appear J. of Geometric Analysis.

Daskalopoulos, Georgios; Mese, Chikako. Uniqueness of equivariant harmonic maps to symmetric spaces and buildings. To appear Mathematical Research Letters.

Daskalopoulos, Georgios; Mese, Chikako; On the singular set of a nonlinear degenerate PDE arising in Teichmueller theory. Proceedings of the American Mathematical Society 150 (2022) 411-422.

Daskalopoulos, Georgios; Mese, Chikako; Rigidity of Teichmueller space. Inventiones Math. 224, (2021), 791-916 

Daskalopoulos, Georgios; Mese, Chikako; Essential Regularity of the Model Space for the Weil-Petersson Metric. Journal fur die reine und angewandte Mathematik (Crelles Journal), Issue 750, (2019), 53-96.

Daskalopoulos, Georgios; Mese, Chikako; Sanders Adrew; Vdovina Alina; Surface groups acting on CAT(-1) spaces. Ergodic Theory and Dynamical Systems, vol 39, Issue 7, (2019), 1843-8564 .

Daskalopoulos, Georgios; Mese, Chikako; Wilkin, Graeme; Higgs bundles over cell complexes and representations of finitely presented groups. Pacific J. of Math. Vol 296, no 1, (2018), 31-55.

Daskalopoulos, Georgios; Mese, Chikako; C1-Estimates for the Weil-Petersson Metric.Transactions of the AMS 369 (2017), 2917-2950.

Daskalopoulos, Georgios; Mese, Chikako; On the Singular Set of Harmonic Maps into DM-Complexes. Memoirs of the American Math. Soc. Vol 239, no 1129, (2016).

Daskalopoulos, Georgios; Mese, Chikako; Monotonicity Properties of Harmonic maps into NPC spaces. J. Fixed Point Theory Appl. 11 (2012) 225-243.

Daskalopoulos, Georgios; Mese, Chikako; Vdovina Alina; Superrigidity of Hyperbolic Buildings. GAFA Vol. 21 (2011) 905-919.

Daskalopoulos, Georgios; Weitsman Jonathan; Wentworth, Richard; Wilkin Graeme; Morse theory and hyperkaehler Kirwan surjectivity for Higgs bundles. J. Diff. Geom. 87 (2011) 81-115.

Daskalopoulos, Georgios; Wentworth, Richard; Wilkin Graeme; Cohomology of SL(2, C) Character varieties of surface groups and the action of the Torelli group. Asian Jour. of Math. Vol 14, no3, pp.359-384, (2010).

Daskalopoulos, Georgios; Mese, Chikako Harmonic Maps between singular spaces I. Communications in Analysis and Geometry Volume 18, Number 2 (2010), 257-337. 

Daskalopoulos, Georgios; Mese, Chikako Fixed point and rigidity theorems for harmonic maps from simplicial complexes into NPC spaces. Geom Dedica (2009) 141:33-57.

Daskalopoulos, Georgios; Mese, Chikako Harmonic maps from a simplicial complex and geometric rigidity. J. Differential Geom. 78 (2008) 269-293.

Daskalopoulos, Georgios; Mese, Chikako Harmonic maps from 2-complexes. Comm. Anal. Geom. 14 (2006), no. 3, 497-549. 

Daskalopoulos, Georgios; Wentworth, Richard Holomorphic frames for weakly converging holomorphic vector bundles. Canad. Math. Bull. 49 (2006), no. 1, 36-40. 

Daskalopoulos, Georgios; Wentworth, Richard Convergence properties of the Yang-Mills flow on Kähler surfaces. Journal fur die reine und angewandte Mathematik (Crelles Journal) 575 (2004), 69-99. 

Daskalopoulos, Georgios; Wentworth, Richard Classification of Weil-Petersson isometries. Amer. J. Math. 125 (2003), no. 4, 941-975. 

Daskalopoulos, Georgios; Wentworth, Richard The Yang-Mills flow near the boundary of Teichmüller space. Math. Ann. 318 (2000), no. 1, 1-42. 

Daskalopoulos, Georgios; Katzarkov, Ludmil; Wentworth, Richard Harmonic maps to Teichmüller space. Math. Res. Lett. 7 (2000), no. 1, 133-146.

Daskalopoulos, Georgios; Dostoglou, Stamatis; Wentworth, R. On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups. Duke Math. J. 101 (2000), no. 2, 189-207.

Daskalopoulos, Georgios; Wentworth, Richard. On the Brill-Noether problem for vector bundles. Forum Math. 11 (1999), no. 1, 63-77.

Daskalopoulos, Georgios; Dostoglou, Stamatis; Wentworth, Richard. Character varieties and harmonic maps to R-trees. Math. Res. Lett. 5 (1998), no. 4, 523-53.

Daskalopoulos, Georgios; Wentworth, Richard. Geometric quantization for the moduli space of vector bundles with parabolic structure. Geometry, topology and physics (Campinas, 1996), 119-155, de Gruyter, Berlin, 1997. 

Daskalopoulos, Georgios.; Dostoglou, Stamatis; Wentworth, Richard. Families of SU(2) representations for mapping cylinders of periodic monodromy. Proc. Edinburgh Math. Soc. (2) 40 (1997), no. 2, 383-392.

Bradlow, Steven; Daskalopoulos, Georgios; Wentworth, Richard. Birational equivalences of vortex moduli. Topology 35 (1996), no. 3, 731-748. 

Daskalopoulos, Georgios; Wentworth, Richard. Factorization of rank two theta functions. II. Proof of the Verlinde formula. Math. Ann. 304 (1996), no. 1, 21-51. 

Bertram, Aaron; Daskalopoulos, Georgios; Wentworth, Richard. Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians. J. Amer. Math. Soc. 9 (1996), no. 2, 529-571. 

Daskalopoulos, Georgios; Uhlenbeck, Karen; Wentworth, Richard. Moduli of extensions of holomorphic bundles on Kähler manifolds. Comm. Anal. Geom. 3 (1995), no. 3-4, 479-522.

Bradlow, Steven; Daskalopoulos, Georgios; García-Prada, Oscar; Wentworth, Richard. Stable augmented bundles over Riemann surfaces. Vector bundles in algebraic geometry (Durham, 1993), 15-67, London Math. Soc. Lecture Note Ser., 208, Cambridge Univ. Press, Cambridge, 1995. 

Daskalopoulos, Georgios; Uhlenbeck, Karen. An application of transversality to the topology of the moduli space of stable bundles. Topology 34 (1995), no. 1, 203-215.

Bradlow, Steven; Daskalopoulos, Georgios. Moduli of stable pairs for holomorphic bundles over Riemann surfaces. II. Internat. J. Math. 4 (1993), no. 6, 903-925.

Daskalopoulos, Georgios; Wentworth, Richard. Local degeneration of the moduli space of vector bundles and factorization of rank two theta functions. I. Math. Ann. 297 (1993), no. 3, 417-466.

Daskalopoulos, Georgios; Wentworth, Richard. The integrability criterion in SU(2) Chern-Simons gauge theory. Comm. Math. Phys. 151 (1993), no. 3, 437-445. 

Daskalopoulos, Georgios The topology of the space of stable bundles on a compact Riemann surface. J. of  Diff. Geom. 36 (1992), no. 3, 699-746. 

Bradlow, Steven; Daskalopoulos, Georgios Moduli of stable pairs for holomorphic bundles over Riemann surfaces. Internat. J. Math. 2 (1991), no. 5, 477-513.

EXPOSITORY ARTICLES:

Daskalopoulos, Georgios; Mese, Chikako: Notes on Harmonic Maps. To appear in the conference proceedings, 2022 Grenoble Summer School, “Non-Abelian Hodge Theory” (arXiv:2301.04190)

Daskalopoulos, Georgios; Wentworth, Richard.  Harmonic maps and Teichmueller theory. Handbook of Teichmueller theory. Vol. I, IRMA Lect. Math. Theor. Phys., 11, Eur. Math. Soc., Zurich, (2007) 33--109.