mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost...

geometry and pseudoholomorphic curves in symplectic geometry: Geodesics are curves of shortest length (locally), while pseudoholomorphic curves are surfaces...

class in X {\displaystyle X} . Then one may consider the set of pseudoholomorphic curves ( ( C , j ) , f , ( x 1 , … , x n ) ) {\displaystyle ((C,j),f,(x_{1}...

pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which...

invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The...

if they are connected via one or more pseudoholomorphic curves. Gromov–Witten invariants, which count these curves, appear as coefficients in expansions...

introduced the notion of hyperbolic groups.[G87] Gromov's theory of pseudoholomorphic curves is one of the foundations of the modern study of symplectic geometry...

In geometry and topology, trivial cylinders are certain pseudoholomorphic curves appearing in certain cylindrical manifolds. In Floer homology and its...

the distribution of values of a holomorphic curve in the complex projective line. Pseudoholomorphic curve Shiffman (1977), p.553 Min Ru (2001). Nevanlinna...

These considerations play a fundamental role in the theory of pseudoholomorphic curves and Gromov–Witten theory. (Note that for this example, the definition...