相关论文: Smooth functions with simple structures on 3-dimen…

Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in C^N (N greater than or equal to 2), of codimension one or more in C^N, and endowed with the induced CR structure. Assuming that the tangential…

This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as…

We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension…

This paper studies the approximation of generalized ridge functions, namely of functions which are constant along some submanifolds of $\mathbb{R}^N$. We introduce the notion of linear-sleeve functions, whose function values only depend on…

The class of special generic maps contains Morse functions with exactly two singular points, characterizing spheres topologically which are not $4$-dimensional and the $4$-dimensional unit sphere. This class is for higher dimensional…

Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…

We consider normalized univalent functions with prescribed second Taylor coefficient $a_2$. For convex functions $f$ we study the Hardy spaces to which $f$ and $f'$ belong, refining in particular on a theorem of Eenigenburg and Keogh, and…

Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…

We prove that almost every level set of a Sobolev function in a planar domain consists of points, Jordan curves, or homeomorphic copies of an interval. For monotone Sobolev functions in the plane we have the stronger conclusion that almost…

Trivalent $2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where three sheets meet. We develop operations on their associated labeled graphs that will effectively construct from a single…

Recently, the forward-backward and Douglas-Rachford envelope functions were proposed in the literature. The stationary points of these envelope functions have a close relationship with the solutions of the possibly nonsmooth optimization…

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…

From a sufficiently large point sample lying on a compact Riemannian submanifold of Euclidean space, one can construct a simplicial complex which is homotopy-equivalent to that manifold with high confidence. We describe a corresponding…

This is an overview article. In his Habilitationsvortrag, Riemann described infinite dimensional manifolds parameterizing functions and shapes of solids. This is taken as an excuse to describe convenient calculus in infinite dimensions…

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $\R^d$, equipped with power weights $w(x) = |x|^\gamma$, $\gamma>-d$. We prove two-weight Sobolev embeddings for these spaces. Moreover, we…

This article proposes to integrate two Reeb graphs with the information of their isosurfaces' inclusion relation. As computing power evolves, there arise numerical data that have small-scale physics inside larger ones -- for example, small…

Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…

In this paper we construct complete simply connected minimal surfaces with a prescribed coordinate function. Moreover, we prove that these surfaces are dense in the space of all minimal surfaces with this coordinate function (with the…

We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two…