Broadly speaking, my research is in geometric analysis: conformal geometry, partial differential equations, the calculus of variations, and global differential geometry.
My full publication list is at MathSciNet.
X. Cao, M. J. Gursky, and H. Tran, "Curvature of the Second kind and a conjecture of Nishikawa", https://arxiv.org/abs/2112.01212
M. J. Gursky and S. Perez-Ayala, " Variational Properties Of The Second Eigenvalue Of The Conformal Laplacian," to appear in J. Funct. Anal., https://arxiv.org/abs/2010.13210
M. J. Gursky, S. McKeown, and A. Tyrrell, "Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces," https://arxiv.org/abs/2101.11755
M. J. Gursky and S. Zhang, "Rigidity for Bach-flat metrics on manifolds with boundary and applications", https://arxiv.org/abs/2007.04355
M. J. Gursky, Q. Han, and S. Stolz, "An invariant related to the existence of conformally compact Einstein fillings", Trans. Amer. Math. Soc. 374 (2021), no. 6, 4185–4205, https://arxiv.org/abs/1801.04474
C. R. Graham and M. J. Gursky, "Chern-Gauss-Bonnet formula for singular Yamabe metrics in dimension four," Indiana Univ. Math. J. 70 (2021), no. 3, 1131–1166, https://arxiv.org/abs/1902.01562
M. J. Gursky, C. Kelleher, and J. Streets, "Index-energy estimates for Yang-Mills connections and Einstein metrics’’, Comm. Math. Phys. 376 (2020), no. 1, 117–143, http://arxiv.org/abs/1901.04539
S.Y.A Chang, M.J Gursky, and S. Zhang," A conformally invariant gap theorem characterizing CP2 via the Ricci flow", Math. Z. 294 (2020), no. 1-2, 721–746, https://arxiv.org/abs/1809.05918
M. J. Gursky and G. Szekelyhidi, " A Local Existence Result for Poincare-Einstein metrics", Adv. Math. 361 (2020), https://arxiv.org/abs/1712.04017
M. J. Gursky and J. Streets, "A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow’’, Geometric Flows, 4 (2019), no. 1, 30-50, https://arxiv.org/abs/1507.04781
M. J. Gursky and J. Streets, "Variational structure of the $v_{\frac{n}{2}}$-Yamabe problem’’, Differential Geom. Appl. 56 (2018), 187–201. https://www.sciencedirect.com/science/article/pii/S0926224517301122
M. J. Gursky, C. Kelleher, and J. Streets, "A conformally invariant gap theorem in Yang-Mills theory’’, Comm. Math. Physics, 361 (2018), 1155-1167 https://link.springer.com/article/10.1007/s00220-017-3070-z
M. J. Gursky and J. Streets, "A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_{2}$-Yamabe problem’’, Geom. & Topology. 22 (2018), 3501-3573 https://arxiv.org/abs/1603.07005
M. J. Gursky and Q. Han, "Non-existence of Poincaré-Einstein manifolds with prescribed conformal infinity’’, Geom. Funct. Anal. 27 (2017), no. 4, 863--879. https://link-springer-com.proxy.library.nd.edu/article/10.1007%2Fs00039-017-0414-y