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Showing 1 to 8 of 8 for “"conformal geometry"”.
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Integrability in random conformal geometry
… in many statistical physics models. Liouville conformal field theory (LCFT) is the quantum field theory underlying LQG. Each of these satisfies conformal invariance or covariance. This thesis proves exact formulas in random conformal geometry; we highlight a few here. The Brownian annulus …
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Homomorphisms of semi-holonomic verma modules : an exceptional case.
… of G, then there is often a differential geometry for which the homogeneous space G/P represents the flat model. An example is conformal geometry, where G is the special orthogonal group SO(n, C). A Verma module homomorphism will corresponds to an invariant operator on the flat space. The …
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Random conformally covariant metrics in the plane
This thesis is in the broad area of random conformal geometry, combining tools from probability and complex analysis. We mainly consider *Liouville quantum gravity* (LQG), a model introduced in the physics literature in the 1980s by Polyakov in order to provide a canonical example of a random …
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Conformal pseudo-metrics and some applications
… connected to a number of basic open problems in conformal geometry and non-linear PDE. One of our results is a solution to Problem 1 for arbitrary simply connected domains. However, we shall see that our approach has also some other ramifications, for instance to a well-known problem due to …
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Conformal Properties of Spacetime
… we study more generally the nature of possible conformal completions at spatial infinity. In particular, we show that (d + 1) dimensional Myers-Perry metrics (d ≥ 4) have a conformal completion at spatial infinity of C^{d−3,1} differentiability class, and that this result is optimal in even …
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PERFECT FLUIDS AND SIGMA MODELS: A MATHEMATICAL INVESTIGATION BETWEEN GENERAL RELATIVITY AND COTTON GRAVITY
… that such structures might give to Riemannian Geometry. In Chapter 1 we fix the notations and conventions and review some of the basics of Riemannian Geometry and General Relativity. We begin Chapter 2 by introducing the theory of Cotton Gravity and showing how it preserves the solutions of …
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Domain filling circle packings
Verallgemeinerungen bekannter Existenz- und Eindeutigkeitsaussagen für gebietsfüllende Kreispackungen. Für jedes beschränkte, einfach zusammenhängende Gebiet und für jeden zulässigen Komplex existiert eine gebietsfüllende, verallgemeinerte Kreispackung, die einer beliebigen der folgenden …
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Topics in Weyl geometry and quantum anomalies
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms