scholarly journals Intrinsic geometry and De Giorgi classes for certain anisotropic problems

2017 ◽  
Vol 10 (4) ◽  
pp. 647-659 ◽  
Author(s):  
Paolo Baroni ◽  
◽  
Agnese Di Castro ◽  
Giampiero Palatucci ◽  
Keyword(s):  
Intrinsic Geometry ◽  
Anisotropic Problems

scholarly journals Coarse median algebras: the intrinsic geometry of coarse median spaces and their intervals

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Graham A. Niblo ◽  
Nick Wright ◽  
Jiawen Zhang
Keyword(s):  
Finite Rank ◽  
Intrinsic Geometry ◽  
Bounded Geometry ◽  
Higher Dimensional ◽  
Median Algebra ◽  
Asymptotic Geometry ◽  
Median Operator

AbstractThis paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra which simultaneously generalises the concepts of bounded geometry coarse median spaces and classical discrete median algebras. We study the coarse median universe from the perspective of intervals, with a particular focus on cardinality as a proxy for distance. In particular we prove that the metric on a quasi-geodesic coarse median space of bounded geometry can be constructed up to quasi-isometry using only the coarse median operator. Finally we develop a concept of rank for coarse median algebras in terms of the geometry of intervals and show that the notion of finite rank coarse median algebra provides a natural higher dimensional analogue of Gromov’s concept of $$\delta $$ δ -hyperbolicity.

The Intrinsic Geometry of the Cerebral Cortex

1994 ◽  
Vol 166 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Lewis D. Griffin
Keyword(s):  
Cerebral Cortex ◽  
Intrinsic Geometry

Intrinsic geometry of Lax equation

2003 ◽  
Vol 6 (3) ◽  
pp. 291-299
Author(s):  
Carlo Cattani ◽  
Ettore Laserra
Keyword(s):  
Intrinsic Geometry ◽  
Lax Equation

scholarly journals Intrinsic Geometry and Analysis of Diffusion Processes and L ∞-Variational Problems

2014 ◽  
Vol 214 (1) ◽  
pp. 99-142 ◽  
Author(s):  
Pekka Koskela ◽  
Nageswari Shanmugalingam ◽  
Yuan Zhou
Keyword(s):  
Diffusion Processes ◽  
Variational Problems ◽  
Intrinsic Geometry

Shape Synthesis and Optimization Using Intrinsic Geometry

1990 ◽  
Author(s):  
Shahriar Tavakkoli ◽  
Sanjay G. Dhande
Keyword(s):  
Optimization Problems ◽  
Piecewise Linear ◽  
Shape Design ◽  
Arc Length ◽  
Intrinsic Geometry ◽  
Shape Model ◽  
Design Variables ◽  
Dimensional Shape ◽  
Variable Geometry Truss ◽  
Arc Lengths

Abstract The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc length. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a pre-specified position and orientation of the end-effector. In conclusion, it can be said that the proposed approach requires fewer design variables as compared to the methods where shape is represented using spline-like functions.

Complex Curves — Origins and Intrinsic Geometry

1994 ◽  
pp. 39-50
Author(s):  
J. J. Gray
Keyword(s):  
Intrinsic Geometry ◽  
Complex Curves

Intrinsic geometry of curves and the Minkowski force

1979 ◽  
Vol 74 (6) ◽  
pp. 381-383 ◽  
Author(s):  
Harry I. Ringermacher
Keyword(s):  
Intrinsic Geometry

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

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