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The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but th ...
In recent years, freeform shapes are gaining more and more popularity in architecture. Such shapes are often challenging to manufacture, and have motivated an active research field called architectural geometry. In this thesis, we investigate patterns of s ...
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...
During the last 20 years, the joint expansion of computing power, computer graphics, networking capabilities and multiresolution analysis have stimulated several research domains, and developed the need for new types of data such as 3D models, i.e. discret ...
We study conditions under which a point of a Riemannian surface has a neighborhood that can be parametrized by polar coordinates. The point under investigation can be a regular point or a conical singularity. We also study the regularity of these polar coo ...
On the identity component of the universal Teichmuller space endowed with the Takhtajan-Teo topology, the geodesics of the Weil Petersson metric are shown to exist for all time. This component is naturally a subgroup of the quasisymmetric homeomorphisms of ...
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...
In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods hav ...
