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Showing 1 to 10 of 10 for “"Holomorphic curves"”.
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J - holomorphic curves and their applications
… an analog of Whitney's embedding theorem for J-holomorphic discs. 2. For zj = xj + i*yj in C and let D_R^2 = {(z1, z2) in C^2 : x1^2 + x2^2 <1, y1^2 + y2^2 < 1} be the real bi-disc in C^2. We find the sharp lower bound for R such that D_R^2 admits a symplectic embedding into D(R) * C, the …
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Compactness results for pseudo-holomorphic curves in symplectic cobordisms
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.
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Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
… intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, …
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Open strings in the cotangent bundle and Morse homotopy
… 3. We study the genus zero open rigid J-holomorphic curves in T*M with boundaries mapped in perturbations of the zero section. The perturbations of the zero section is defined fixing a. set of functions on M. We consider the graphs of the differential of the functions rescaled by an …
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On contact homology of the unit cotangent bundle of a Riemann surface with genus greater than one
In this thesis, I study pseudo-holomorphic curves in symplectisation of the unit cotangent bundle of a Riemann surface of genus greater than 1. The contact form and compatible almost complex structure are both constructed from a metric on the Riemann surface whose curvature is constant -1. I …
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Geometry of SU(3) Manifolds
… dual instantons; The third is pseudo-holomorphic curves.</p><p>For the first perspective, I am interested in the interplay between $SU(3)$ structures and their special Lagrangian submanifolds. More precisely, I study $SU(3)$-structures which locally support as `nice' special Lagrangian …
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Some Results on the Degeneracy of Entire Curves and Integral Points in the Complements of Divisors
… we extend the Second Main Theorem to the case of holomorphic curves into algebraic varieties intersecting numerically equivalent ample divisors. In chapter 4, we improve Ru's defect relation (see \cite{ru15}) and the height inequality (see \cite{ru}) in the case when $X$ is a normal projective …
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An elementary approach to some aspects of Heegaard Floer homology
… by Ozsvath and Szabo. It counts pseudo-holomorphic Whitney disks in the symmetric product of the Heegaard surface of the underlying manifold. This thesis is about showing the existence of a natural complex structure on the symmetric product Sym9 (E9) of a surface E9 and mainly studying …
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Aspects Of Phenomenology And Cosmology In Heterotic M-Theory
… that M-theory admits five-branes, which wrap holomorphic curves upon dimensional compactification. We construct an effective N=1 supersymmetric action to describe the world-volume theory of the resulting three-branes, which live in the bulk space of heterotic M-theory.
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Computations in monotone Floer theory
… their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian dynamics, and more recently it has become a major component of the Homological Mirror Symmetry conjecture. This work presents several new computations in …