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Conformal maps from a 2-torus to the 4-sphere
Space is immersed generalized modular space immersed ring Riemann surface spectral curve
2014/12/25
We study the space of conformal immersions of a 2-torus into the 4-sphere. The moduli space of generalized Darboux transforms of such an immersed torus has the structure of a Riemann surface, the spec...
The spectral curve of a quaternionic holomorphic line bundle over a 2-torus
Riemann surface the spectral curve curve four yuan dirichlet energy
2014/12/24
A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain Dirac type operator o...
Random walk on a discrete torus and random interlacements
Random walk discrete torus random interlacements
2009/3/19
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)d, d ≥ 3, until u Nd time steps, u > 0, and the model of random interlacements r...