On complete stable minimal surfaces in 4-manifolds with positive isotropic curvature - Mathematics > Differential GeometryReportar como inadecuado




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Abstract: We prove the nonexistence of stable immersed minimal surfaces uniformlyconformally equivalent to the complex plane in any complete orientablefour-dimensional Riemannian manifold with uniformly positive isotropiccurvature. We also generalize the same nonexistence result to higher dimensionsprovided that the ambient manifold has uniformly positive complex sectionalcurvature. The proof consists of two parts, assuming an -eigenvalue condition-on the Cauchy-Riemann operator of a holomorphic bundle, we prove 1 avanishing theorem for these holomorphic bundles on the complex plane; 2 anexistence theorem for holomorphic sections with controlled growth byHormander-s weighted L^2-method.



Autor: Martin Li

Fuente: https://arxiv.org/







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