- In mathematics,
specifically in
topology and geometry, a
pseudoholomorphic curve (or J-holomorphic curve) is a
smooth map, from a
Riemann surface into...
-
geometry and
pseudoholomorphic curves in
symplectic geometry:
Geodesics are
curves of
shortest length (locally),
while pseudoholomorphic curves are surfaces...
-
invariants are
rational numbers that, in
certain situations,
count pseudoholomorphic curves meeting prescribed conditions in a
given symplectic manifold...
-
homology class in X {\displaystyle X} . Then one may
consider the set of
pseudoholomorphic curves ( ( C , j ) , f , ( x 1 , … , x n ) ) {\displaystyle ((C,j)...
- More precisely, they
intersect if they are
connected via one or more
pseudoholomorphic curves. Gromov–Witten invariants,
which count these curves, appear...
-
symplectic topology and
gauge theory, and they are
known for work on
pseudoholomorphic quilts. With Dusa McDuff, they have
challenged the
foundational rigor...
- loops) to the
symplectic manifold of interest;
solutions are
known as
pseudoholomorphic curves. The
Gromov compactness theorem is then used to show that the...
- and
general relativity Institutions Princeton University Thesis Pseudoholomorphic Curves in
Almost Complex Manifolds (1999)
Doctoral advisor Lev Vil'evich...
- the
product of spheres, can be
computed using Gromov's
theory of
pseudoholomorphic curves.
Unlike Riemannian manifolds,
symplectic manifolds are not...
- Mean
curvature flow
Minimal submanifolds Positive energy theorems Pseudoholomorphic curves Ricci flow
Yamabe problem Yang–Mills
equations Jackson, Allyn...
