1,720,986 research outputs found
CIME school “Fully Nonlinear PDEs in Real and Complex Geometry and Optics”
No full textThe purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari
Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Caratheodory metrics
No full text
A subelliptic analogue of Aronson–Serrin’s Harnack inequality
Full text linkWe show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE associated to a system of Lipschitz continuous Hormander vector fields follows from the basic hypothesis of doubling condition and a weak Poincar\'e inequality
Ahlfors type estimates forperimeter measures in Carnot-Carathéodory spaces
No full textWe study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theorems for perimeter estimates between an hypersurface and its tangent space, and between a CC geometry and its tangent Carnot group structure
Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups
Full text linkIn this paper we study heat kernels associated with a Carnot
group G, endowed with a family of collapsing left-invariant
Riemannian metrics σε which converge in the Gromov-
Hausdorff sense to a sub-Riemannian structure on G as ε→
0. The main new contribution are Gaussian-type bounds on
the heat kernel for the σε metrics which are stable as ε→0
and extend the previous time-independent estimates in [16].
As an application we study well posedness of the total variation
flow of graph surfaces over a bounded domain in a step
two Carnot group (G; σε ). We establish interior and boundary
gradient estimates, and develop a Schauder theory which are
stable as ε → 0. As a consequence we obtain long time
existence of smooth solutions of the sub-Riemannian flow
(ε = 0), which in turn yield sub-Riemannian minimal surfaces
as t → ∞
SUB-RIEMANNIAN HEAT KERNELS AND MEAN CURVATURE FLOW OF GRAPHS.
Full text linkWe introduce a sub-Riemannian analogue of the Bence-Merriman-Osher algorithm (Merriman et al., 1992 [42]) and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the nonlinear semi-group theory approach originally introduced by L.C. Evans (1993) [27] in the Euclidean setting and is based on new results on the relation between sub-Riemannian heat flows of characteristic functions of subgraphs and the horizontal mean curvature of the corresponding graph
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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