Gromov's tori are optimal
Anton Petrunin
TL;DR
This paper establishes the best possible bounds on the normal curvatures of immersed n-dimensional tori within high-dimensional Euclidean balls, advancing understanding of geometric constraints for such immersions.
Contribution
It provides the first optimal bounds on normal curvatures for immersed tori in high-dimensional Euclidean spaces.
Findings
Derived the sharpest bounds on normal curvatures for immersed tori.
Demonstrated these bounds are optimal and cannot be improved.
Extended geometric analysis to high-dimensional Euclidean balls.
Abstract
We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds