Search results for "tangent"
showing 10 items of 123 documents
Triangular Bézier Approximations to Constant Mean Curvature Surfaces
2008
We give a method to generate polynomial approximations to constant mean curvature surfaces with prescribed boundary. We address this problem by finding triangular Bezier extremals of the CMC-functional among all polynomial surfaces with a prescribed boundary. Moreover, we analyze the $\mathcal{C}^1$ problem, we give a procedure to obtain solutions once the tangent planes for the boundary curves are also given.
Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application
2014
Abstract We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations.
Self-affine sets with fibered tangents
2016
We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal O$ such that all tangent sets at that point are either of the form $\mathcal O((\mathbb R \times C) \cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times \{ 0 \}) \cap B(0,1))$, where $\ell$ is an interval.
Blending canal surfaces along given circles using Dupin cyclides
2013
We study blends between canal surfaces using Dupin cyclides via the space of spheres. We have already studied the particular case where it is possible to blend two canal surfaces using one piece of Dupin cyclide bounded by two characteristic circles, but this is not possible in the general case. That is why we solve this problem using two pieces of different cyclides, which is always possible. To get this conclusion and give the algorithms allowing to obtain such a result, we study, at first, the blend between two circles by a piece of cyclide. We impose to the cyclide to be tangent to a given sphere containing one of the circles. We give the existence condition on the previous circles to h…
Local Gromov-Witten invariants are log invariants
2019
We prove a simple equivalence between the virtual count of rational curves in the total space of an anti-nef line bundle and the virtual count of rational curves maximally tangent to a smooth section of the dual line bundle. We conjecture a generalization to direct sums of line bundles.
A proof of Carleson's $\varepsilon^2$-conjecture
2019
In this paper we provide a proof of the Carleson $\varepsilon^2$-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson $\varepsilon^2$-square function.
Singularities of rational Bézier curves
2001
We prove that if an nth degree rational Bezier curve has a singular point, then it belongs to the two (n − 1)th degree rational Bezier curves defined in the (n − 1)th step of the de Casteljau algorithm. Moreover, both curves are tangent at the singular point. A procedure to construct Bezier curves with singularities of any order is given. 2001 Elsevier Science B.V. All rights reserved.
Left-Right Equivalence and Stability
2020
We introduce the key equivalence relations on germs of maps, which play an important role throughout the book—right-equivalence and left-right equivalence (A-equivalence). These are induced by groups of diffeomorphisms, so equivalence classes have tangent spaces, and we calculate many examples, including some multi-germs. We introduce the notions of stability and finite determinacy, and prove Mather’s infinitesimal criterion for stability.
Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)
2012
International audience; A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we su…
Actions de IR et courbure de ricci du Fibré unitaire tangent des surfaces
1986
Characterisation of 2-dimensional Riemannian manifolds (M, g) (in particular, of surfaces with constant gaussian curvatureK=1/c2, o,−1/c2, respectively) whose tangent circle bundle (TcM, gs) (gs=Sasaki metric) admit an «almost-regular» vector field belonging to an eigenspace of the Ricci operator.