# Matthew J. Gursky

Professor

B.S., University of Michigan, 1986

Ph.D., California Institute of Technology, 1991

Email: Matthew.J.Gursky.1@nd.edu

Office: 262 Hurley Hall

Phone: (574) 631-8848

Fax: (574) 631-6579

**Research Interests**

Broadly speaking, my research is in geometric analysis: conformal geometry, partial differential equations, the calculus of variations, and global differential geometry.

Some of my recent work has focused on fully nonlinear elliptic equations in conformal geometry. The solvability of these equations and estimates of solutions are strongly influenced by the topology and geometry of the underlying manifold, especially in low dimensions. This connection has resulted in some interesting applications to the geometry of four-manifolds.

**Selected Publications**

- M.J. Gursky, The Weyl functional, de Rham cohomology, and K\"ahler—Einstein metrics,
*Annals of Math.***148**(1998), 315—337.

- M.J. Gursky and C. LeBrun, Yamabe constants and spin$^c$ structures,
*GAFA*8 (1998), 965—977.

- M.J. Gursky, The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE,
*Comm. Math. Phys.***207**(1999), 131—143.

- M.J. Gursky, Four—manifolds with $\delta W^+=0$ and Einstein constants of the sphere,
*Math. Annalen***318**(2000), 417—431.

- M.J. Gursky and J. Viacolvsky, A new variational characterization of three-dimensional space forms,
*Invent. Math.***145**(2001), 251—278.

- S.-Y.A. Chang, M.J. Gursky, and P. Yang, An equation of Monge- Ampere type in conformal geometry, and four manifolds of positive Ricci curvature,
*Annals of Math.***155**(2002), 711—789.

Please direct questions and comments to: Matthew.J.Gursky.1@nd.edu