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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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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

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