Related papers: Interpolation by maximal and minimal surfaces

We show that a multiplicative form of Dirichlet's theorem on simultaneous Diophantine approximation as formulated by Minkowski, cannot be improved for almost all points on any analytic curve on R^k which is not contained in a proper affine…

A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or "position") of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The…

Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…

Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calder\'on products if both interpolants are separable. We show that one separability assumption may be omitted and establish a…

Modern shape design and capture techniques often lead to the geometric data presented in the form of serial rows of data points. In general, the number of data points varies from row to row. Lofted or skinned B-spline surface interpolation…

We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz's representation theorem.

In color spaces where the chromatic term is given in polar coordinates, the shortest distance between colors of the same value is circular. By converting such a space into a complex polar form with a real-valued value axis, a color algebra…

We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the…

If $X$ is a subset of a Banach space with $X-X$ homogeneous, then $X$ can be embedded into some $\R^n$ (with $n$ sufficiently large) using a linear map $L$ whose inverse is Lipschitz to within logarithmic corrections. More precisely,…

Given an interpolating Blaschke product $B$ with zeros $\{a_j\}$, we seek to characterize the sequences of values $\{w_j\}$ for which the interpolation problem $$f(a_j)=w_j\qquad (j=1,2,\dots)$$ can be solved with a function $f$ from the…

The real interpolation spaces between $L^{p}({\mathbb{R}}^{n})$ and $\dot {H}^{t,p}({\mathbb{R}}^{n})$ (resp. $H^{t,p}({\mathbb{R}}^{n})$), $t>0,$ are characterized in terms of fractional moduli of smoothness, and the underlying seminorms…

We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.

We consider the method of quasi-solutions (also referred to as Ivanov regularization) for the regularization of linear ill-posed problems in non-reflexive Banach spaces. Using the equivalence to a metric projection onto the image of the…

The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of these concepts to Borel measures with density in…

The notions of the Euclidean surface area measure and the spherical surface area measure of $\alpha$-concave functions in $\mathbb{R}^n$, with $-\frac{1}{n}<\alpha<0$, are introduced via a first variation of the total mass functional with…

Let $\Omega$ be a bounded, weakly pseudoconvex domain in C^n, n > 1, with real-analytic boundary. A real-analytic submanifold $M \subset bd\Omega$ is called an analytic interpolation manifold if every real-analytic function on M extends to…

Let $X$ be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed $L$-Lipschitz curve $\gamma:S^1\rightarrow X$ may be extended to an $L$-Lipschitz map defined on the…

Building upon Bennett's and Grosse-Erdmann's ideas falling under the conceptual umbrella of factorization of inequalities, we propose a unified approach towards the structure of certain Banach ideal spaces defined in terms of the least…

Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair…

We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the…