Related papers: A Flat Strip Theorem for Ptolemaic Spaces
In this paper, we consider a Generalized Bernstein Theorem for a type of generalized minimal surfaces, namely minimal Plateau surfaces. We show that if an orientable minimal Plateau surface is stable and has quadratic area growth in…
We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.
In this paper, we prove a rigidity theorem for smooth strictly convex domains in Euclidean spaces.
We prove the following result. Let f be a continuous function in the closed infinite strip in complex plane. Suppose the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle. Then f is…
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…
Desuspension Theorem for the steam $\Pi_{2^l-2}$ in stable homotopy groups of spheres is formulated and is proved. The proof is a minor revision of a theorem in the preprint \cite{A1} by the author (2010).
We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.
In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.
We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…
We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of…
We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.
We generalize the notion of flat chains with arbitrary coefficient groups to Banach spaces and prove a sequential compactness result. We also remove the restriction that a flat chain have finite mass in order for its support to exist.
We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero,…
We show that a refined version of Golyshev's canonical strip hypothesis does hold for the Hilbert polynomials of complete intersections in rational homogeneous spaces.
This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note…
We prove a formula that expresses the Viterbo-Maslov index of a smooth strip in an oriented 2-manifold with boundary curves contained in 1-dimensional submanifolds in terms the degree function on the complement of the union of the two…
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders…