3,200 research outputs found
Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds
No full text
Periodic Solutions of Semilinear Multivalued and Functional Evolution Equations in Banach Spaces
No full textThis paper deals with the semilinear multivalued evolution equationx'(t) + A(t)x(t) Є F(t, x(t)), t Є [a, b] and x Є E,in an arbitrary Banach space E.The linear operators {A(t) : t Є [a, b]} are densely defined on a common domain in E and generate a strongly continuous evolution system. We discuss the existence of mild periodic solutions, also in the case when the nonlinear term F depends on aretarded argument. We also show that in both cases the solutions set is compact. The proofs are based on topological arguments and make use of the theory of condensing multimaps
The positive mass theorem and distance estimates in the spin setting
No full textLet E \mathcal {E} be an asymptotically Euclidean end in an otherwise arbitrary connected Riemannian spin manifold ( M , g ) (M,g) . We show that if E \mathcal {E} has negative ADM-mass, then there exists a constant R > 0 R > 0 , depending only on E \mathcal {E} , such that M M must become incomplete or have a point of negative scalar curvature in the R R -neighborhood around E \mathcal {E} in M M . This gives a quantitative answer to Schoen and Yau’s question on the positive mass theorem with arbitrary ends for spin manifolds. Similar results have recently been obtained by Lesourd, Unger and Yau [ Positive scalar curvature on noncompact manifolds and the liouville theorem , 2020; The positive mass theorem with arbitrary ends , 2021] without the spin condition in dimensions ≤ 7 \leq 7 assuming Schwarzschild asymptotics on the end E \mathcal {E} . We also derive explicit quantitative distance estimates in case the scalar curvature is uniformly positive in some region of the chosen end E \mathcal {E} . Here we obtain refined constants reminiscent of Gromov’s metric inequalities with scalar curvature
Renforcer la protection sociale: L’expérience de l’Amérique latine et des Caraïbes
Full text linkLa protection sociale est apparue durant ces dernières années comme un axe à partir duquel il est prévu d’intégrer une série de mesures visant à garantir des niveaux de vie fondamentaux pour tous et à construire des sociétés plus équitables et plus inclusives. En particulier, la protection sociale s’inscrit dans le cadre d’une politique fondamentale pour accélérer les progrès vers les objectifs de développement durable (ODD).
Le but de ce livre est d’offrir aux lecteurs les bases conceptuelles de la protection sociale et des connaissances sur les politiques publiques, les programmes et les cadres réglementaires qui, à partir d’une approche fondée sur les droits, permettent de promouvoir une plus grande égalité sociale et d’élargir la couverture de protection sociale tout au long du cycle de vie en Amérique latine et dans les Caraïbes.
La réalisation de ce livre s’insère dans l’intense travail de coopération technique de la CEPALC visant à accompagner et soutenir le cheminement d’Haïti vers un développement durable. En particulier, il s’agit d’une contribution au processus de réflexion sur la nécessité et l’urgence de construire un véritable système de protection sociale.Avant-propos .-- Introduction / Simone Cecchini, Randolph Gilbert, Beatriz Morales .--- Partie 1. Protection sociale inclusive en Amérique latine et les Caraïbes: un regard intégral, une approche fondée sur les droits --- I. La politique et la protection sociale / Simone Cecchini, Rodrigo Martínez .-- II. La protection sociale en Amérique latine dans le nouveau millénaire / Simone Cecchini, Rodrigo Martínez .-- III. L’approche fondée sur les droits en matière de protection sociale / Simone Cecchini, María Nieves Rico .-- IV. Vers un système intégral de protection sociale / Simone Cecchini, Rodrigo Martínez --- Partie 2. Vers une protection sociale universelle: instruments de politique au long du cycle de vie .-- V. La petite enfance et l’enfance / Cecilia Rossel, María Nieves Rico, Fernando Filgueira .-- VI. L’adolescence et la jeunesse / Cecilia Rossel, Fernando Filgueira .-- VII. Étape active et reproductive / Cecilia Rossel, Fernando Filgueira .-- VIII. Personnes âgées / Cecilia Rossel, Fernando Filgueira .-- IX. Les soins, un pilier de la protection sociale: droits, politiqueset institutions en Amérique latine / María Nieves Rico, Claudia Robles --- Partie 3. Éléments clés pour renforcer la protection sociale .-- X. Suivi et évaluation des politiques et programmes de protection sociale / Rodrigo Matínez .-- XI. Le financement et l’investissement en matière de protection sociale / Fernando Filgueira, Rodrigo Martíne
A long neck principle for Riemannian spin manifolds with positive scalar curvature
No full textWe develop index theory on compact Riemannian spin manifolds with boundary in the case when the topological information is encoded by bundles which are supported away from the boundary. As a first application, we establish a “long neck principle” for a compact Riemannian spin n-manifold with boundary X, stating that if scal(X)≥n(n−1) and there is a nonzero degree map into the sphere f:X→Sn which is strictly area decreasing, then the distance between the support of df and the boundary of X is at most π/n. This answers, in the spin setting and for strictly area decreasing maps, a question recently asked by Gromov. As a second application, we consider a Riemannian manifold X obtained by removing k pairwise disjoint embedded n-balls from a closed spin n-manifold Y. We show that if scal(X)>σ>0 and Y satisfies a certain condition expressed in terms of higher index theory, then the radius of a geodesic collar neighborhood of ∂X is at most π(n−1)/(nσ)−−−−−−−−−−√. Finally, we consider the case of a Riemannian n-manifold V diffeomorphic to N×[−1,1], with N a closed spin manifold with nonvanishing Rosenebrg index. In this case, we show that if scal(V)≥σ>0, then the distance between the boundary components of V is at most 2π(n−1)/(nσ)−−−−−−−−−−√. This last constant is sharp by an argument due to Gromov.Georg-August-Universität Göttingen (1018
Nonnegative scalar curvature on manifolds with at least two ends
No full textLet
be an orientable connected
-dimensional manifold with
and let
be a two-sided closed connected incompressible hypersurface that does not admit a metric of positive scalar curvature (abbreviated by psc). Moreover, suppose that the universal covers of
and
are either both spin or both nonspin. Using Gromov's
-bubbles, we show that
does not admit a complete metric of psc. We provide an example showing that the spin/nonspin hypothesis cannot be dropped from the statement of this result. This answers, up to dimension 7, a question by Gromov for a large class of cases. Furthermore, we prove a related result for submanifolds of codimension 2. We deduce as special cases that, if
does not admit a metric of psc and
, then
does not carry a complete metric of psc and
does not carry a complete metric of uniformly psc, provided that
and
, respectively. This solves, up to dimension 7, a conjecture due to Rosenberg and Stolz in the case of orientable manifolds.Studienstiftung des Deutschen Volkes http://dx.doi.org/10.13039/501100004350Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/50110000165
Rozpor ako východisko, láska ako smer u Simone Weilovej (Contradiction as base, Love as direction in writings of Simone Weil)
No full textArticle is explaining contradiction and love, Simone Weil‘s essential terms of hermeneutics of human Being. It introduces close relation of these terms with her understanding of God as well as with her overall concept of religion. Author also mentions Simone Weil‘s inspirations with philosophical and spiritual concepts of the East
Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shields
Full text linkWe prove a positive mass theorem for spin initial data sets that
contain an asymptotically flat end and a shield of dominant energy (a subset of
on which the dominant energy scalar has a positive lower bound).
In a similar vein, we show that for an asymptotically flat end
that violates the positive mass theorem (i.e. ),
there exists a constant , depending only on , such that any
initial data set containing must violate the hypotheses of
Witten's proof of the positive mass theorem in an -neighborhood of
. This implies the positive mass theorem for spin initial data
sets with arbitrary ends, and we also prove a rigidity statement. Our proofs
are based on a modification of Witten's approach to the positive mass theorem
involving an additional independent timelike direction in the spinor bundle.Comment: 18 page
Lipschitz rigidity for scalar curvature
No full textLet M be a closed smooth connected spin manifold of even dimension n , let g be a Riemannian metric of regularity W^{1,p} , p > n , on M whose distributional scalar curvature in the sense of Lee–LeFloch is bounded below by n(n-1) , and let f \colon (M,g) \to \mathbb{S}^n be a 1 -Lipschitz continuous (not necessarily smooth) map of nonzero degree to the unit n -sphere. Then f is a metric isometry. This generalizes a result of Llarull (1998) and answers in the affirmative a question of Gromov (2019) in his Four lectures . Our proof is based on spectral properties of Dirac operators for low regularity Riemannian metrics and twisted with Lipschitz bundles. We argue that the existence of a nonzero harmonic spinor field forces f to be quasiregular in the sense of Reshetnyak, and in this way connect the powerful theory for quasiregular maps to the Atiyah–Singer index theorem
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