5 papers · 1 filter
Non-uniqueness of geodesic limits and a question of Grayson and Gage
Shrey Aryan, Tang-Kai Lee
Grayson and Gage proved that an immortal curve shortening flow of simple closed curves on a closed surface converges subsequentially to a closed geodesic, and they asked whether th…
Calabi-Yau Conjecture for Minimal Hypersurfaces in with bounded geometry
Shrey Aryan, Alexander D. McWeeney, Giuseppe Tinaglia
The Calabi-Yau conjectures for complete minimal hypersurfaces for ask whether a complete minimal hypersurface must be unbounded, and more…
Half-Space Theorem for Minimal Hypersurfaces in
Shrey Aryan, Alexander D. McWeeney
The three-dimensional catenoid in is a complete embedded minimal hypersurface contained in a slab, showing that the half-space theorem does not extend directly to hi…
Spectral Obstructions to Contracting Transport Maps on Curved Spaces
Shrey Aryan
Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is -Lipschitz. Motiva…
On the Calabi-Yau Conjectures for Minimal Hypersurfaces in Higher Dimensions
Shrey Aryan, Alexander D. McWeeney
In this paper, we study the Calabi-Yau conjectures for complete minimal hypersurfaces in dimensions . These conjectures ask whether a compl…