Unknotted Reeb orbits and nicely embedded holomorphic curves
نویسندگان
چکیده
منابع مشابه
J−holomorphic Curves and Periodic Reeb Orbits *
We study the J−holomorphic curves in the symplectization of the contact manifolds and prove that there exists at least one periodic Reeb orbits in any closed contact manifold with any contact form by using the well-known Gromov's nonlinear Fredholm alternative for J−holomorphic curves. As a corollary, we give a complete solution on the well-known Weinstein conjecture.
متن کاملArea Inequalities for Embedded Disks Spanning Unknotted Curves
We show that a smooth unknotted curve in R3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giving the upper bound on the area grows exponentially in 1/r2. In the direction ...
متن کاملThe embedded contact homology index revisited
Let Y be a closed oriented 3-manifold with a contact form such that all Reeb orbits are nondegenerate. The embedded contact homology (ECH) index associates an integer to each relative 2-dimensional homology class of surfaces whose boundary is the difference between two unions of Reeb orbits. This integer determines the relative grading on ECH; the ECH differential counts holomorphic curves in t...
متن کاملHolomorphic Curves and Toda Systems *
Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex and quaternionic projective spaces or complex quadrics. The paper generalizes the well known connection between minimal surfaces in E3, their Wei...
متن کاملHolomorphic Curves from Matrices
Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static solutions to the matrix theory equations of motion, and which can be interpreted as the matrix theory representation of the holomorphically embedded membrane. Th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symplectic Geometry
سال: 2020
ISSN: 1527-5256,1540-2347
DOI: 10.4310/jsg.2020.v18.n1.a2