Related papers: A Structure-Preserving Numerical Method for Harmon…
Non-polynomial growth harmonic maps from the complex plane to the hyperbolic space are studied. Some non-surjectivity results are obtained. Moreover, images of such harmonic maps are investigated with reference to their Hopf differentials.
We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.
Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one…
We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section space of a projective bundle, and show that it induces an…
We prove that for any open Riemann surface $N,$ natural number $n\geq 3,$ non-constant harmonic map $h:N\to \mathbb{R}^{n-2}$ and holomorphic 2-form $H$ on $N,$ there exists a weakly complete harmonic map $X=(X_j)_{j=1,\ldots,n}:N \to…
In this paper, we introduce the discrete conformal structures on surfaces with boundary in an axiomatic approach, which ensures that the Poincar\'{e} dual of an ideally triangulated surface with boundary has a good geometric structure.Then…
We give a more geometric approach to an algorithm for deciding whether two hyperbolic 3-manifolds are homeomorphic. We also give a more algebraic approach to the homeomorphism problem for geometric, but non-hyperbolic, 3-manifolds.
In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relatively simple behaviour it was known that such a classification…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
Scene graph representations enable structured visual understanding by modeling objects and their relationships, and have been widely used for multiview and 3D scene reasoning. Existing methods such as MSG learn scene graph embeddings in…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
We propose a harmonic surface mapping algorithm (HSMA) for electrostatic pairwise sums of an infinite number of image charges. The images are induced by point sources within a box due to a specific boundary condition which can be…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
We classify weakly complete constant Gaussian curvature $-1<K<0$ surfaces in the hyperbolic three-space in terms of holomorphic quadratic differentials. For this purpose, we first establish a loop group method for constant Gaussian…
Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate…
We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
Accurate segmentation of tubular structures in medical images, such as vessels and airway trees, is crucial for computer-aided diagnosis, radiotherapy, and surgical planning. However, significant challenges exist in algorithm design when…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…