22,554 research outputs found
Recommended from our members
Modified Ricci flow on a principal bundle
No full texttextLet M be a Riemannian manifold with metric g, and let P be a principal G-bundle over M having connection one-form a. One can define a modified version of the Ricci flow on P by fixing the size of the fiber. These equations are called the Ricci Yang-Mills flow, due to their coupling of the Ricci flow and the Yang-Mills heat flow. In this thesis, we derive the Ricci Yang-Mills flow and show that solutions exist for a short time and are unique. We study obstructions to the long-time existence of the flow and prove a compactness theorem for pointed solutions. We represent the Ricci Yang-Mills flow as a gradient flow and derive monotonicity formulas that can be used to study breather and soliton solutions. Finally, we use maximal regularity theory and ideas of Simonett concerning the asymptotic behavior of abstract quasilinear parabolic partial differential equations to study the stability of the Ricci Yang-Mills flow in dimension 2 at Einstein Yang-Mills metrics.Mathematic
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]
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
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
Introduzione [a Il viaggio di P. Matteo Ricci]
No full textIntroduzione al volume pubblicato per il centenario di Matteo Ricci a Macerata
Un percorso all'interno del manuale (in Peter STOTZ - Francesco SANTI - Paolo GARBINI - Luigi G. G. RICCI, Il latino nel Medioevo nella visione di Peter Stotz - Verona, 22 maggio 2014. STUDI MEDIEVALI, vol. 55, p. 653-682)
No full textThe article is composed of four presentations. P. Stotz illustrates
the genesis and the intentions of his Handbuch zur Sprache des lateinischen
Mittelalters, based on the census and the study of a number of linguistic facts and
expressive conventions, which are documented in the Latin of the Middle
Ages. The heuristic principles that have guided the work are argued. F. Santi
notes the importance of the conclusions of Stotz about the vitality of Latin in
the Middle Ages and the variety of performances that for the Latin language
were tested in the Middle Ages; it is placed in relation to some literary
situations and to plurilinguistic condition of the medieval culture. P. Garbini
detects the systematic approach and the intelligent and open problematic of the
survey conducted by Stotz, which offers much more than it promises: the
Handbuch posed in new and polishes terms the issue of continuity /
discontinuity of the Latin language between Antiquity and the Middle Ages, as
well as the theme of the vitality of Latin in the Middle Ages. L. Ricci proposes
a path of study inside the Handbuch devoted to the theme of the Latin
Christians from Antiquity to the Renaissance, focusing in particular on some
examples in the attitude of the Humanists regard to the Latin of the Bible, also
proposing a comparison between the text of the Vulgata and the translation by
Sebastian Castellio (1515-1563)
PhD Thesis - Ricci - Supplementary Materials
No full textSupplementary Materials for the PhD Thesis of Alejandro Daniel Ricci</p
The Moments of the Density of Zeros for the Relativistic Hermite and Laguerre Polynomials
No full textAbstractThe moments of the density of zeros of two new orthogonal polynomial systems, called Relativistic Hermite Polynomials {H(N)n (ξ)}∞n=0 (RHP) and Relativistic Laguerre Polynomials {L(α,N)n (ξ)}∞n=0 (RLP), are represented by means of a Cases' method and of a representation formula, introduced by Ricci, in terms of generalized Lucas polynomials of the second kind. By using a FORTRAN program, numerical computations are explicitly developed in some particular case
- …
