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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Frozen elephant trunk: Assets and liabilities of a challenging technique

The development of the frozen elephant trunk (FET) technique for a simplified treatment of complex lesions of the thoracic aorta originated as an evolution of the classic elephant trunk technique, described for the first time by Borst et al .[1] in 1983. Novel technologies and standardization of the surgical approach produced a progressive improvement of early and late outcomes. Most of the time and for specific indications, FET procedure allows physicians to treat lesions involving extensive portions of the thoracic aorta in one single step. Spinal cord injury remains one of the main complications of this procedure, even though spinal protection strategies have led to better results. We hereby report our opinions and recommendations based on our experience started in 2007

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

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