The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface

Details The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface

1997-10-07

arxiv.org/abs/dg-ga/9710005v1

Asian J. Math. 1(1997) 230-248

Mathematics

Differential Geometry

26 pages, Latex, to appear in Asian J. Math. 1(1997) No. 2

Scientific paper

Let $M$ be a compact Riemann surface, $h(x)$ a positive smooth function on
$M$. In this paper, we consider the functional $$J(u)={1/2}\int
\sb{M}|\bigtriangledown u|\sp 2 + 8\pi \int\sb{M}u -8\pi \log\int\sb{M}h\exp
{u}$$. We give a sufficient condition under which $J$ achieves its minimum.

Affiliated with

Also associated with

No associations

Rating

The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The differential equation $Δu = 8π- 8πh\exp {u}$ on a compact Riemann surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203822