Search Results - "Gursky, Matthew"

Non-existence of Poincaré–Einstein manifolds with prescribed conformal infinity by Gursky, Matthew J., Han, Qing

“…In this note we prove the existence of infinitely many positive conformal classes on S 7 which cannot be the conformal infinity of a Poincaré–Einstein metric…”
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Index-Energy Estimates for Yang–Mills Connections and Einstein Metrics by Gursky, Matthew J., Kelleher, Casey Lynn, Streets, Jeffrey

“…We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical…”
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Prescribing Symmetric Functions of the Eigenvalues of the Ricci Tensor by Gursky, Matthew J., Viaclovsky, Jeff A.

“…We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem…”
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An Equation of Monge-Ampère Type in Conformal Geometry, and Four-Manifolds of Positive Ricci Curvature by Chang, Sun-Yung A., Gursky, Matthew J., Yang, Paul C.

“…We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality…”
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CONFORMAL INVARIANTS ASSOCIATED TO A MEASURE: CONFORMALLY COVARIANT OPERATORS by CHANG, Sun-Yung A, GURSKY, Matthew J, YANG, Paul

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Conformal Invariants Associated to a Measure by Chang, Sun-Yung A., Gursky, Matthew J., Yang, Paul

“…In this note, we study some conformal invariants of a Riemannian manifold ($M^{n}$, g) equipped with a smooth measure m. In particular, we show that there is a…”
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A non-local flow for Riemann surfaces by Gursky, Matthew J.

“…A non-local flow is defined for compact Riemann surfaces. Assuming the initial metric has positive Gauss curvature and is not conformal to the round sphere,…”
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Fully Nonlinear Equations on Riemannian Manifolds with Negative Curvature by Gursky, Matthew J., Viaclovsky, Jeff A.

“…It is proved that every compact Riemannian manifold of dimension n ≥ 3 with negative Ricci curvature is conformal to a metric with det(Ric) = constant. This is…”
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Volume comparison and the σk-Yamabe problem by Gursky, Matthew J, Viaclovsky, Jeff A

“…In this paper we study the problem of finding a conformal metric with the property that the kth elementary symmetric polynomial of the eigenvalues of its…”
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Renormalized volume and non-degeneracy of conformally compact Einstein four-manifolds by Gursky, Matthew J.

“…In this article we give a condition, depending on the renormalized volume of a four-dimensional Poincaré-Einstein manifold, which implies that the…”
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An a priori estimate for a fully nonlinear equation on four-manifolds by Chang, Sun-Yung A., Gursky, Matthew J., Yang, Paul

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A new variational characterization of three-dimensional space forms by Gursky, Matthew J., Viaclovsky, Jeff A.

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Convexity and singularities of curvature equations in conformal geometry by Gursky, Matthew J., Viaclovsky, Jeff

“…We define a generalization of convex functions, which we call δ-convex functions, and show that they must satisfy interior Hölder and W1,p estimates. As an…”
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Curvature of the second kind and a conjecture of Nishikawa by Cao, Xiaodong, Gursky, Matthew J., Tran, Hung

“…In this paper we investigate manifolds for which the curvature operator of the second kind (following the terminology of Nishikawa (1986)) satisfies certain…”
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A Conformally Invariant Gap Theorem in Yang–Mills Theory by Gursky, Matthew, Kelleher, Casey Lynn, Streets, Jeffrey

“…We show a sharp conformally invariant gap theorem for Yang–Mills connections in dimension 4 by exploiting an associated Yamabe-type problem…”
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Variational properties of the second eigenvalue of the conformal Laplacian by Gursky, Matthew J., Pérez-Ayala, Samuel

“…Let (Mn,g) be a closed Riemannian manifold of dimension n≥3. Assume [g] is a conformal class for which the Conformal Laplacian Lg has at least two negative…”
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The Weyl Functional, de Rham Cohomology, and Kähler-Einstein Metrics by Gursky, Matthew J.

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Critical metrics on connected sums of Einstein four-manifolds by Gursky, Matthew J., Viaclovsky, Jeff A.

“…We develop a gluing procedure designed to obtain canonical metrics on connected sums of Einstein four-manifolds. The main application is an existence result,…”
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Non-uniqueness Results for Critical Metrics of Regularized Determinants in Four Dimensions by Gursky, Matthew, Malchiodi, Andrea

“…The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994 ), IV.4. γ ]. An explicit formula…”
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On Einstein Manifolds of Positive Sectional Curvature by Gursky, Matthew J, LeBrun, Claude

“…Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form and g has non-negative sectional curvature, we show…”
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