Geometry and Topology

In this thesis, we study some results of f-minimal surfaces in product spaces with the following purposes: State the relation between the f-minimal surfaces and the selfsimilar solutions of the mean curvature flow; state some properties of the f-minimal surfaces in the product spaces; construct some Bernstein type theorems, halfspace type theorems for f-minimal (f-maximal) surfaces in product spaces; state some results on the higher codimensional f-minimal surfaces.

28p closefriend09 16-11-2021 20 3   Download

Objectives of research: The thesis is to give and prove some uniaueness theorems of the meromorphic functions f(z) on the complex plane which has hyperorder plane less than 1 share a part of the values with its f(z + c).

27p thebadguys 08-06-2021 18 4   Download

In this paper we will discuss the geometry of finite topology properly embedded minimal surfaces M in R3 . M of finite topology means M is homeomorphic to a compact surface M (of genus k and empty boundary) minus a finite number of points p1 , ..., pj ∈ M , called the punctures. A closed neighborhood E of a puncture in M is called an end of M . We will choose the ends sufficiently small so they are topologically S 1 × [0, 1) and hence, annular. We remark that M is orientable since M is properly...

33p noel_noel 17-01-2013 61 6   Download

The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in Orlik-Terao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n-cells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...

36p tuanloccuoi 04-01-2013 240 8   Download