球面上具有四个不同主曲率的Moebius等参超曲面

设x:M→S~(n+1)(n≥5)是(n+1)-维单位球面上不含脐点的超曲面,在S~(n+1)的Moebius变换群下浸入x的四个基本不变量是:Moebius度量g;Moebius第二基本形式B;Moebius形式Φ和Blaschke张量A.本文给出S~(n+1)上具有重数1,1,1,m(m≥2)的四个不同Moebius主曲率的Moebius等参超曲面的分类.     

Fermat point for a triangle in three dimensions using the taxicab metric

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.     

Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

We consider a planar Riemann surface R made of a non‐compact simply connected plane domain from which an infinite discrete set of points is removed. We give several conditions for the collars of the cusps in R caused by these points to be uniformly distributed in R in terms of Euclidean geometry. Then we associate a graph G with R by taking the Voronoi diagram for the uniformly distributed cusps and show that G represents certain geometric and analytic properties of R .     

Gonality of complete graphs with a small number of omitted edges

Let be the complete metric graph on d vertices. We compute the gonality of graphs obtained from by omitting edges forming a , or general configurations of at most edges. We also investigate if these graphs can be lifted to curves with the same gonality. We lift the former graphs and the ones obtained by removing up to edges not forming a K ₃ using models of plane curves with certain singularities. We also study the gonality when removing edges not forming a K ₃. We use harmonic morphism to lift these graphs to curves with the same gonality because in this case plane singular models can no longer be used due to a result of Coppens and Kato.     

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmüller space AT(D) are studied in this paper. It is proved that if μ is asymptotically extremal in [[μ]] with h_ζ~*(μ) h~*(μ) for some point ζ∈ ?D, then there exist infinitely many geodesic segments joining [[0]]and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [[μ]] in AT(D).     

Multi Fuzzy Fractal Theorems in Fuzzy Metric Spaces

The Hutchinson-Barnsley (HB) operators are studied for multi iterated function system in a general setting. Some existence and uniqueness results are obtained in fuzzy fractal and multi fuzzy fractal spaces. From them, we obtain our results, which generalize some recent results in the literature.     

带权散度型椭圆算子的低阶特征值估计

本文首先给出紧致带边(边界可以为空集)光滑度量测度空间上带权散度型算子的低阶特征值的一个一般不等式,通过使用这个一般不等式,可以得到光滑度量测度空间中有界连通区域上带权散度型算子的低阶特征值的一些万有不等式.     

Hölder Continuity of Random Processes

For a Young function φ and a Borel probability measure m on a compact metric space (T,d) the minorizing metric is defined by

Equivariant deformations of LeBrun's self-dual metrics with torus action

We investigate -equivariant deformations of C. LeBrun's self-dual metric with torus action. We explicitly determine all -subgroups of the torus for which one can obtain -equivariant deformations that do not preserve the whole of the torus action. This gives many new self-dual metrics with -action which are not conformally isometric to LeBrun metrics. We also count the dimension of the moduli space of self-dual metrics with -action obtained in this way.

     

Weil-Petersson isometries via the pants complex

We extend a theorem of Masur-Wolf which states that given a finite-area hyperbolic surface , every isometry of the Teichmüller space for with the Weil-Petersson metric is induced by an element of the mapping class group for . Our argument handles the previously untreated cases of the four times-punctured sphere, the once-punctured torus, and the twice-punctured torus.