Related papers: Embedding Some Riemann Surfaces into \C^2 with Int…

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…

We prove several interpolation results for holomorphic Legendrian curves lying in an odd dimensional complex Euclidean space with the standard contact structure. In particular, we show that an arbitrary countable set of points in…

Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…

We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…

In this short note we describe a simple adaptation of biharmonic surfaces to interpolate boundary cross-derivatives given in ribbon form, and compare with the recently proposed Generalized B-spline patches.

In this paper, we investigate the interpolation of surfaces which are obtained from an isoasymptotic curve in 3D-Euclidean space. We prove that there exist a unique $ C^0 $-Hermite surface interpolation related to an isoasymptotic curve…

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…

We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.

This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…

This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…

All previously published work on isomorphic grid embeddings into n-cubes has been restricted to binary n-cubes. This paper describes a straightforward method for embedding a A x B grid isomorphically into a k-ary n-cube with k>2.

We review classical approaches to the problem of isometrically embedding a Riemannian surface into Euclidean 3-space, including coordinate-based approaches exposited by Darboux and Eisenhart, as well as the moving-frames based approaches…

In the paper we prove integral formulae for a Riemannian manifold endowed with $k>2$ orthogonal complementary distributions, which generalize well-known formula for $k=2$ and give applications to splitting and isometric immersions of…

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…

To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.

Certain semi-Riemannian metrics may be decomposed into a Riemannian part and an isochronal part. We use this idea and an idea of Kasner to construct a manifold in 6+1 Minkowski space with a well known metric. The full embedding we display…

A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…

In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…