137,545 research outputs found
L-optimal transportation for Ricci flow
No full textWe introduce the notion of L-optimal transportation, and use it to construct a natural monotonic quantity for Ricci flow which includes a selection of other monotonicity results, including some key discoveries of Perelman [13] (both related to entropy and to L-length) and a recent result of McCann and the author [11]
Ricci flow coupled with harmonic map flow
No full text07.02.13 KB. Accepted version ok to add to Spiral. SMF/SherpaWe investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive coupling constant alpha. This system can be interpreted as the gradient flow of an energy functional F_alpha which is a modification of Perelman's energy F for the Ricci flow, including the Dirichlet energy for the map phi. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of phi a-priori - without any assumptions on the curvature of the target manifold N - by choosing alpha large enough. Moreover, if alpha is bounded away from zero it suffices to bound the curvature of (M,g(t)) to also obtain control of phi and all its derivatives - a result which is clearly not true for alpha = 0. Besides these new phenomena, the flow shares many good properties with the Ricci flow. In particular, we can derive the monotonicity of an entropy functional W_alpha similar to Perelman's Ricci flow entropy W and of so-called reduced volume functionals. We then apply these monotonicity results to rule out non-trivial breathers and geometric collapsing at finite times
On Type-I singularities in Ricci flow
No full text07.02.13 KB. Accepted version ok to add to Spiral. IP/Sherpa.We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow
Instantaneously complete Ricci flows on surfaces
No full textThe intention of this thesis is to give a survey of instantaneously complete Ricci
flows
on surfaces, focussing on the existence and uniqueness of its Cauchy problem. We
prove a general existence result for instantaneously complete Ricci
flows starting at
an arbitrary Riemannian surface which may be incomplete and may have unbounded
curvature. We give an explicit formula for the maximal existence time, and describe
the asymptotic behaviour in most cases. The issue of uniqueness within this class of
instantaneously complete Ricci
flows is still conjectured but we are going to describe
the progress towards its proof. Finally, we apply that new existence result in order to
construct an immortal complete Ricci
flow which has unbounded curvature for all time
The volume entropy of a surface decreases along the Ricci flow
No full textThe volume entropy, h(g), of a compact Riemannian manifold (M,g) measures the growth rate of the volume of a ball of radius R in its universal cover. Under the Ricci flow, g evolves along a certain path that improves its curvature properties. For a compact surface of variable negative curvature we use a Katok–Knieper–Weiss formula to show that h(gt) is strictly decreasing
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Analysis of Ricci flow on noncompact manifolds
No full texttextIn this dissertation, we present some analysis of Ricci flow on complete noncompact manifolds. The first half of the dissertation concerns the formation of Type-II singularity in Ricci flow on [mathematical equation]. For each [mathematical equation] , we construct complete solutions to Ricci flow on [mathematical equation] which encounter global singularities at a finite time T such that the singularities are forming arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate [mathematical equation]. Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton. As an application of this result, we prove that there exist standard solutions of Ricci flow on [mathematical equation] whose blow-ups near the origin converge uniformly to the Bryant soliton. In the second half of the dissertation, we fully analyze the structure of the Lichnerowicz Laplacian of a Bergman metric g[subscript B] on a complex hyperbolic space [mathematical equation] and establish the linear stability of the curvature-normalized Ricci flow at such a geometry in complex dimension [mathematical equation]. We then apply the maximal regularity theory for quasilinear parabolic systems to prove a dynamical stability result of Bergman metric on the complete noncompact CH[superscript m] under the curvature-normalized Ricci flow in complex dimension [mathematical equation]. We also prove a similar dynamical stability result on a smooth closed quotient manifold of [mathematical symbols]. In order to apply the maximal regularity theory, we define suitably weighted little Hölder spaces on a complete noncompact manifold and establish their interpolation properties.Mathematic
Determination of the Beryllium neutrino flux from helioseismic data
No full textWe show that helioseismology provides information on Beryllium neutrino production in the Sun. In particular, we derive a lower limit on the Beryllium neutrino flux on earth, ΦminBe = 1 · 109 cm-2s-1, in the absence of oscillations, by using helioseismic data, the B-neutrino flux measured by Superkamiokande and the hydrogen abundance at the solar center predicted by Standard Solar Models. Moreover, we obtain an helioseismic determination of ΦBe by comparing solar model with artificially changed νBe production with helioseismic data. © 2001 Elsevier Science B.V
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Camillo Ricci
No full textSi tratta della biografia del pittore ferrarese Camillo Ricci allievo dello Scarsellino. Viene presentato anche l'inventario dei suoi beni nel quale sono elencati diversi dipinti
Determination of the Beryllium neutrino flux from helioseismic data
No full textWe show that helioseismology provides information oil Beryllium neutrino production in the Sun. ill particular, we derive a lower limit oil the Beryllium neutrino flux on earth. Phi (min)(Be) = 1 . 10(9)cm(-2)s(-1), in the absence of oscillations. by using helioseismic data, the B-neutrino flux measured by Superkamiokande and the hydrogen abundance at the solar center predicted by Standard Solar Models. Moreover. we obtain an helioseismic determination of Phi (Be) by comparing solar model with artificially changed v(Bc) production with helioseismic data
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