scholarly journals Prescribing Gaussian curvature on closed Riemann surface with conical singularity in the negative case

2019 ◽  
Vol 44 (1) ◽  
pp. 167-181 ◽  
Author(s):  
Yunyan Yang ◽  
Xiaobao Zhu
Keyword(s):  
Riemann Surface ◽  
Gaussian Curvature ◽  
Conical Singularity ◽  
Negative Case ◽  
Closed Riemann Surface

HARMONIC MAPS FROM A CLOSED SURFACE OF HIGHER GENUS TO THE UNIT 2-SPHERE

1993 ◽  
Vol 04 (02) ◽  
pp. 359-365 ◽  
Author(s):  
GUOFANG WANG
Keyword(s):  
Riemann Surface ◽  
Harmonic Maps ◽  
Closed Surface ◽  
Higher Genus ◽  
Closed Riemann Surface

We obtain the existence of harmonic maps of degree one from a closed Riemann surface of genus greater than 1 with a metric admitting a plane of symmetry to the unit 2-sphere.

Covering properties of open continuous mappings having two valences between Riemann surfaces

1995 ◽  
Vol 118 (2) ◽  
pp. 321-340 ◽  
Author(s):  
Abdallah Lyzzaik
Keyword(s):  
Riemann Surface ◽  
Finite Number ◽  
Riemann Surfaces ◽  
Embedding Theorem ◽  
Branch Points ◽  
Continuous Mappings ◽  
Counting Multiplicity ◽  
Covering Properties ◽  
Closed Riemann Surface ◽  
Finite Genus

AbstractLet be an open Riemann surface with finite genus and finite number of boundary components, and let be a closed Riemann surface. An open continuous function from to is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in either p or q times, counting multiplicity, with possibly a finite number of exceptions. These comprise the most general class of all non-trivial functions having two valences between and .The object of this paper is to study the geometry of (p, q)-maps and establish a generalized embedding theorem which asserts that the image surfaces of (p, q)-maps embed in p-fold closed coverings possibly having branch points off the image surfaces.

BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES

2010 ◽  
Vol 21 (04) ◽  
pp. 475-495 ◽  
Author(s):  
YUXIANG LI ◽  
YOUDE WANG
Keyword(s):  
Riemannian Manifold ◽  
Riemann Surface ◽  
Critical Points ◽  
Homotopy Class ◽  
Blow Up ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Energy Identity ◽  
Minimal Point ◽  
Closed Riemann Surface

Let f be a positive smooth function on a closed Riemann surface (M, g). The f-energy of a map u from M to a Riemannian manifold (N, h) is defined as [Formula: see text] and its L2-gradient is: [Formula: see text] We will study the blow-up properties of some approximate f-harmonic map sequences in this paper. For a sequence uk : M → N with ‖τf(uk)‖L2 < C1 and Ef(uk) < C2, we will show that, if the sequence is not compact, then it must blow-up at some critical points of f or some concentrate points of |τf(uk)|2dVg. For a minimizing α-f-harmonic map sequence in some homotopy class of maps from M into N we show that, if the sequence is not compact, the blow-up points must be the minimal point of f and the energy identity holds true.

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