scholarly journals On the normal exponential map in singular conformal metrics

2015 ◽  
Vol 127 ◽  
pp. 35-44 ◽  
Author(s):  
Roberto Giambò ◽  
Fabio Giannoni ◽  
Paolo Piccione
Keyword(s):  
Exponential Map ◽  
Conformal Metrics

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

New Parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and Some Explicit Formulas for Its Logarithm

2021 ◽  
Vol 60 ◽  
pp. 65-81
Author(s):  
Tihomir Valchev ◽  
◽  
Clementina Mladenova ◽  
Ivaïlo Mladenov
Keyword(s):  
Lie Groups ◽  
Analytic Description ◽  
Exponential Map ◽  
Explicit Formulas ◽  
Field Of Values

Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $\mathrm{Sp}(2,\bbr)\cong\mathrm{SL}(2,\bbr)$. Relying on the properties of the exponential map $\mathfrak{sl}(2,\bbr)\to\mathrm{SL}(2,\bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups.\\ Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.

Blowing up with infinite energy of conformal metrics on Sn

1999 ◽  
Vol 24 (5-6) ◽  
pp. 785-799 ◽  
Author(s):  
Chiun-Chuan Chen ◽  
Chiun-Chuan Chen ◽  
Chang-Shou Lin ◽  
Chang-Shou Lin
Keyword(s):  
Conformal Metrics ◽  
Blowing Up ◽  
Infinite Energy
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