Seminars and Colloquia
Mathematics
Conformal metrics on R n with arbitrary total Q -curvature
Mon, Jul 17, 2017,
04:30 PM to 05:30 PM
at Madhava Hall
Dr. Ali Hyder
The university of Basel, Switzerland
Abstract
I will talk about the existence of solution to the
Q
-curvature problem
(
−
∆)
n
2
u
=
Qe
nu
in
R
n
, κ
:=
∫
R
n
Qe
nu
dx <
∞
,
(1)
where
Q
is a non-negative function and
n >
2. Geometrically, if
u
is a solution to
(1) then
Q
is the
Q
-curvature of the conformal metric
g
u
=
e
2
u
|
dx
|
2
(
|
dx
|
2
is the
Euclidean metric on
R
n
), and
κ
is the total
Q
-curvature of
g
u
.
Under certain assumptions on
Q
around origin and at infinity, we prove the
existence of solution to (1) for every 0
κ
