Sergey
Grigorian,
Simons
Center
for
Geometry
and
Physics
“Short-time
behaviour
of
a
modified
Laplacian
coflow
of
G2-structures”
We
first
consider
the
Laplacian
co-flow
of
co-closed
G2-structures
on
compact
7-dimensional
manifolds.
This
is
the
heat
flow
for
the
dual
4-form
of
a
G2-structure.
However
this
flow
turns
out
to
be
not
even
weakly
parabolic,
unlike
a
similar
flow
for
the
G2-structure
3-form.
We
then
modify
this
flow
to
make
it
weakly
parabolic
in
the
direction
of
closed
forms
and
prove
short
time
existence
and
uniqueness
of
solutions
for
this
new
flow.