From minimal Lagrangian to J-minimal submanifolds: persistence and uniqueness

Given a minimal Lagrangian submanifold L in a negative Kaehler--Einstein manifold M, we show that any small Kaehler--Einstein perturbation of M induces a deformation of L which is minimal Lagrangian with respect to the new structure. This provides a new source of examples of minimal Lagrangians. More generally, the same is true for the larger class of totally real J-minimal submanifolds in Kaehler manifolds with negative definite Ricci curvature.Comment: Final version, 22 pages; to appear in a special volume in memory of Paolo de Bartolomeis, Boll. UM

Commentary: Aortic valve annuloplasty: The true and the false

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From Lagrangian to totally real geometry: coupled flows and calibrations

We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-K\"ahler case, by its analogues. To this end we explore the geometry of totally real submanifolds, defining (i) a new geometric flow in terms of the ambient canonical bundle, (ii) a modified volume functional which takes into account the totally real condition. We discuss short-time existence for our flow and show it couples well with the Streets-Tian symplectic curvature flow for almost K\"ahler manifolds. We also discuss possible applications to Lagrangian submanifolds and calibrated geometry

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Commentary: Novel interventions in complex aortic disease: A perfect storm to “B-SAFER”

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Total endovascular repair of a malpositioneted frozen elephant trunk with Thoraflex hybrid prosthesis: A case report

We report a case of a 56-year-old male who underwent Frozen Elephant Trunk procedure for residual type A chronic aortic dissection, complicated by the release of the distal endovascular portion of the hybrid prosthesis in the false lumen. This complication was successfully treated with a totally endovascular approach