Alessio Figalli's contributionsto nonlocal minimal surfaces

Serena Dipierro; Enrico Valdinoci

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Free boundary minimal surfaces: a survey of recent results

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From non-Kählerian surfaces to Cremona group of P 2 (C)

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For any minimal compact complex surface S with n = b2(S) > 0 containing global spherical shells (GSS) we study the effectiveness of the 2n parameters given by the n blown up points. There exists a family of surfaces S → B with GSS which contains as fibers S, some Inoue-Hirzebruch surface and non minimal surfaces, such that blown up points are generically effective parameters. These families are versal outside a non empty hypersurface T ⊂ B. We deduce that, for any configuration of...