Related papers: The Endpoint Theorem
Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…
In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…
We show that string theory with Dirichlet boundaries is equivalent to string theory containing surfaces with certain singular points. Surface curvature is singular at these points. A singular point is resolved in conformal coordinates to a…
In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. Unlike for undirected graphs, some ends are joined by limit…
In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…
Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean…
There are different definitions of ends in non-locally-finite graphs which are all equivalent in the locally finite case. We prove the compactness of the end-topology that is based on the principle of removing finite sets of vertices and…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…
The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a…
The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…
Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
In this paper we define a degree for ends of infinite digraphs. The well-definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices…
We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…
In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These…
We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in…
Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…
We establish an existence theory for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoring missing data in an image as steady state of a…
We prove the "End Curve Theorem," which states that a normal surface singularity $(X,o)$ with rational homology sphere link $\Sigma$ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good…