Solutions of the Ginzburg–Landau equations concentrating on codimension‐2 minimal submanifolds
Marco Badran,
Manuel del Pino
Abstract:We consider the magnetic Ginzburg–Landau equations on a closed manifold formally corresponding to the Euler–Lagrange equations for the energy functional
where and is a 1‐form on . Given a codimension‐2 minimal submanifold , which is also oriented and non‐degenerate, we construct solutions such that has a zero set consisting of a smooth surface close to . Away from , we have
as , for all sufficiently small and . Here, is a normal frame for in . This improves a recent result by De Philippis and Pigati (20… Show more
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