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pro vyhledávání: '"Guenther, Christine"'
We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our recent work where sectoriality for the generator of the Ricci-DeTurck fl
Externí odkaz:
http://arxiv.org/abs/2303.04800
We present simple conditions which ensure that a strongly elliptic operator $L$ generates an analytic semigroup on H\"older spaces on an arbitrary complete manifold of bounded geometry. This is done by establishing the equivalent property that $L$ is
Externí odkaz:
http://arxiv.org/abs/2210.15886
We prove that both the Laplacian on functions, and the Lichnerowicz Laplacian on symmetric 2-tensors with respect to asymptotically hyperbolic metrics, are sectorial maps in weighted H\"older spaces. As an application, the machinery of analytic semig
Externí odkaz:
http://arxiv.org/abs/2109.00096
Akademický článek
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Autor:
Carfora, Mauro, Guenther, Christine
Let $(\mathcal{M},g)$ be a closed Riemannian manifold. The $\textit{ second order approximation}$ to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : \[ \frac{\partial }{\partial t} \, g(t) \, =\, -2
Externí odkaz:
http://arxiv.org/abs/1805.09773
The principle of convergence stability for geometric flows is the combination of the continuous dependence of the flow on initial conditions, with the stability of fixed points. It implies that if the flow from an initial state $g_0$ exists for all t
Externí odkaz:
http://arxiv.org/abs/1805.00539
We prove local existence for the second order Renormalization Group flow initial value problem on closed Riemannian manifolds $(M,g)$ in general dimensions, for initial metrics whose sectional curvatures $K_P$ satisfy the condition $1+\alpha K_P > 0$
Externí odkaz:
http://arxiv.org/abs/1401.1454
The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincar\'e Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first order app
Externí odkaz:
http://arxiv.org/abs/1312.6049
We study the behavior of the second order Renormalization Group flow on locally homogeneous metrics on closed three-manifolds. In the cases $\mathbb R^3$ and $\text{SO}(3)\times \R$, the flow is qualitatively the same as the Ricci flow. In the cases
Externí odkaz:
http://arxiv.org/abs/1205.6507
Autor:
Guenther, Christine, Oliynyk, Todd A.
Publikováno v:
Lett.Math.Phys.84:149-157,2008
We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to \cite{GIK02}, where the stability of the
Externí odkaz:
http://arxiv.org/abs/0810.3954