CORDIS Project
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This project explores advanced concepts in geometry and analysis, focusing on scalar curvature and mean curvature flow. It aims to establish new bounds for minimal surfaces in positive scalar curvature manifolds and to address open problems related to minimal Lagrangians in Calabi-Yau manifolds.
The interplay between Geometry and Analysis has been among the most fruitful mathematical ideas in recent years, the most obvious example being Perelman's proof of Poincare' conjecture. I plan to pursue further this approach and make distinct progress in two different problems.Scalar Curvature:
A classical theorem in Riemannian Geometry states that nonnegative scalar curvature metrics which are flat outside a compact set must be Euclidean.
The equivalent problem for positive scalar curvature is…
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