Related papers: The general setting for Shape Analysis

Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…

We generalize the concept of sub-Riemannian geometry to infinite-dimensional manifolds modeled on convenient vector spaces. On a sub-Riemannian manifold $M$, the metric is defined only on a sub-bundle $\calH$ of the tangent bundle $TM$,…

The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric…

The configuration space of a non-linear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on non-linear sigma models with target a homogeneous space. It begins with a description of the…

The present paper is devoted to the study a global aspect of the geometry of harmonic mappings and, in particular, infinitesimal harmonic transformations, and represents the application of our results to the theory of Ricci solutions and…

Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…

This text is an introductory review of the basic concepts of the theory of semi-Riemannian geometry on real finite-dimensional manifolds without boundary.

We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the L\"owner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a…

The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…

The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…

Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between…

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…

Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.…

We obtain a topological interpretation for the space of $L^2$ harmonic forms for some complete Riemannian manifold : when the geometry at infinity is the geometry of a simply connected nilpotent Lie group, when the geometry at infinity is a…

In this work, we systematically treat the ambiguities that generically arise in the gradient expansion of any hydrodynamic theory. While these ambiguities do not affect the physical content of the equations, they induce two types of…

Shape grammars compute over shapes which are defined in the universe $U^*$. Shapes in the universe $U^*$ are analogous to line drawings that can be physically realized in the plane. Any shape is embedded or contained in an arrangement of…

We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…