scholarly journals Ricci curvature in dimension 2

2022 ◽  
Author(s):  
Alexander Lytchak ◽  
Stephan Stadler
Keyword(s):  
Ricci Curvature ◽  
Dimension 2

Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes

1978 ◽  
Vol 84 (1) ◽  
pp. 159-175 ◽  
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich
Keyword(s):  
Ricci Curvature ◽  
Energy Condition ◽  
Cauchy Surface ◽  
Energy Conditions ◽  
Curvature Condition ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Dimension 2 ◽  
Hyperbolic Spacetimes ◽  
Conformal Deformations

AbstractWe consider globally hyperbolic spacetimes (M, g) of dimension ≥ 3 satisfying the curvature condition Ric (g) (v, v) ≥ 0 for all non-spacelike tangent vectors v in TM. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M, g) admits a smooth globally hyperbolic time function h: M → such that for some t0, the Cauchy surface h−1(t0) satisfies the strict curvature condition Ric (g) (v, v) > 0 for all non-spacelike v attached to h−1(t0). Then M admits a metric g′ conformal to g satisfying the strict curvature condition Ric (g′) (v, v) > 0 for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension ≥ 2 and for non-positive Ricci curvature.

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

scholarly journals GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR

2021 ◽  
pp. 1-54
Author(s):  
MANUEL L. REYES ◽  
DANIEL ROGALSKI
Keyword(s):  
Regularity Property ◽  
Graded Algebra ◽  
General Study ◽  
Locally Finite ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Dimension 2 ◽  
Separable Algebras ◽  
Gk Dimension

Abstract This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

scholarly journals Who Gets what and how Does it Matter? Importance-Weighted Portfolio Allocation and Coalition Support in Brazil

2018 ◽  
Vol 10 (3) ◽  
pp. 99-134 ◽  
Author(s):  
Mariana Batista
Keyword(s):  
Positive Relationship ◽  
Portfolio Allocation ◽  
Weighted Portfolio ◽  
Dimension 2 ◽  
Legislative Support ◽  
Presidential Systems

Who gets what in portfolio allocation, and how does it matter to coalition partners’ legislative support in presidential systems? I propose that portfolios are not all alike, and that their allocation as well as the support for the president's agenda depends on the particular distribution of assets within the executive. The portfolio share allocated to coalition parties is weighted by a measure of importance based on the assets controlled by the ministry in question, such as policies, offices, and budgets. Once the weighted allocation of ministries has been identified, the results show that: 1) the president concentrates the most important ministries in their own party, mainly considering the policy dimension; 2) the positive relationship between portfolio allocation and legislative support remains, with the importance of specific dimensions being considered; and, 3) coalition partners do not respond differently in terms of legislative support in light of the different assets’ distribution within the portfolio allocation.

HARNACK-TYPE INEQUALITIES FOR THE POROUS MEDIUM EQUATION ON A MANIFOLD WITH NON-NEGATIVE RICCI CURVATURE

2012 ◽  
Vol 23 (04) ◽  
pp. 1250009 ◽  
Author(s):  
JEONGWOOK CHANG ◽  
JINHO LEE
Keyword(s):  
Porous Medium ◽  
Riemannian Manifold ◽  
Ricci Curvature ◽  
Porous Medium Equation ◽  
Complete Riemannian Manifold ◽  
Gradient Estimates ◽  
Medium Equation

We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.

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