210 research outputs found
Geometric aspects of p-capacitary potentials
No full textWe provide monotonicity formulas for solutions to the p-Laplace equation defined in the exterior of a convex domain. A number of analytic and geometric consequences are derived, including the classical Minkowski inequality as well as new characterizations of rotationally symmetric solutions and domains. The proofs rely on the conformal splitting technique introduced by the second author in collaboration with V. Agostiniani
Comparing monotonicity formulas for electrostatic potentials and static metrics
No full textIn this note we survey and compare the monotonicity formulas recently discovered by the authors in [1] and [2] in the context of classical potential theory and in the study of static metrics, respectively. In both cases we discuss the most significant implications of the monotonicity formulas in terms of sharp analytic and geometric inequalities. In particular, we derive the classical Willmore inequality for smooth compact hypersurfaces embedded in Euclidean space and the Riemannian Penrose inequality for static Black Holes with connected horizon
Scambio di modelli o di oggetti. Analisi archeometriche su ceramiche Serra d'Alto da contesti VBQ in Emilia occidentale
No full textMODEL OF PRODUCTION OF FINISHED POTS EXCHANGE. ARCHAEOMETRIC ANALYSIS OF SERRA D'ALTO POTS FROM SMP SETTLEMENTS IN WESTERN EMILIA. This study aims to explore the issue of circulation in Northern Italy of finished pots of Mid-Late Neolithic ‘Serra d’Alto’ ware, rather than of production model of this ware. The 32 potsherds were analyzed by means of petrographic analysis and they can be divided into 13 different fabrics for their composition and grain-size distribution. Fine ware was produced using local Eocene and Oligocene clays, while almost all the coarse ware was tempered with spatic calcite clasts. The differences observed in thin section point to a common paste processing for fine and coarse wares which must have occurred in different places with different raw materials. The data suggests a polycentric production based on a common technological background. The hypothesis of circulation of finished ceramic pots was not validated while a widespread technological model probably occurred in different areas of Northern and Southern Italy.SCAMBIO DI MODELLI O DI OGGETTI. ANALISI ARCHEOMETRICHE SU CERAMICHE SERRA D'ALTO DA CONTESTI VBQ IN EMILIA OCCIDENTALE. Nella formazione e nello sviluppo delle culture del Neolitico pieno dell’area padana s’intrecciano radici locali, condivisioni di tratti comuni a vasti ambiti culturali ed elementi francamente esogeni, in particolare dal mondo Serra d’Alto, spesso rielaborati e fatti propri. Intento del contributo è verificare sulle produzioni in ceramica figulina rinvenute in contesti emiliani eventuali specifiche affinità di ordine tecnologico con le produzioni Serra d’Alto dell’Italia meridionale, già oggetto di sistematiche indagini archeometriche
On the isoperimetric Riemannian Penrose inequality
No full textWe prove that the Riemannian Penrose inequality holds for asymptotically flat 3-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the (Formula presented.) mass being a well-defined geometric invariant. Our proof builds on a novel interplay between the Hawking mass and a potential-theoretic version of it, recently introduced by Agostiniani, Oronzio, and the third named author. As a consequence, we establish the equality between (Formula presented.) mass and Huisken's isoperimetric mass under the above sharp assumptions. Moreover, we establish a Riemannian Penrose inequality in terms of the isoperimetric mass on any 3-manifold with nonnegative scalar curvature, connected horizon boundary, and which supports a well-posed notion of weak inverse mean curvature flow (IMCF). In particular, such isoperimetric Riemannian Penrose inequality does not require the asymptotic flatness of the manifold. The argument is based on a new asymptotic comparison result involving Huisken's isoperimetric mass and the Hawking mass
Correction to: Implementation and Assessment Methodologies of Teachers’ Training Courses for STEM Activities (Technology, Knowledge and Learning, (2019), 24, 2, (247-268), 10.1007/s10758-018-9356-1)
No full textThe article listed above was initially published with incorrect copyright information. Upon publication of this Correction, the copyright of this article has been changed to “The Author(s)”. The original article has been corrected
Generalized connected sum construction for scalar flat metrics
No full textIn this paper we construct constant scalar curvature metrics on the generalized connected sum of two compact Riemannian scalar flat manifolds (M 1, g 1) and (M 2, g 2) along a common Riemannian submanifold (K, g K ) whose codimension is ≥3. Here we present two constructions: the first one produces a family of “small” (in general nonzero) constant scalar curvature metrics on the generalized connected sum of M 1 and M 2. It yields an extension of Joyce’s result for point-wise connected sums in the spirit of our previous issues for nonzero constant scalar curvature metrics. When the initial manifolds are not Ricci flat, and in particular they belong to the (1+) class in the Kazdan–Warner classification, we refine the first construction in order to produce a family of scalar flat metrics on M. As a consequence we get new solutions to the Einstein constraint equations on the generalized connected sum of two compact time symmetric initial data sets, extending the Isenberg–Mazzeo–Pollack gluing construction
Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
No full textThe notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric assumptions on the ambient manifold, the strictly outward minimising hull Ω⁎ of a set Ω is characterised as a maximal volume solution of the least area problem with obstacle, where the obstacle is the set itself. In the case where Ω has C1,α-boundary, the area of ∂Ω⁎ is recovered as the limit of the p-capacities of Ω, as p→1+. Finally, building on the existence of strictly outward minimising exhaustions, a sharp isoperimetric inequality is deduced on complete noncompact manifolds with nonnegative Ricci curvature, provided 3≤n≤7
On the global structure of conformal gradient solitons with nonnegative Ricci tensor
No full textIn this paper we prove that any complete n-dimensional conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product R x N^(n−1), or globally conformally equivalent to the Euclidean space R^n or to the round sphere S^n. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant
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