The regularity of Special Legendrian Integral Cycles

TL;DR

This paper proves that Special Legendrian Integral Cycles in the 5-sphere are mostly smooth, with potential singularities only at isolated points, advancing understanding of their geometric regularity.

Contribution

It establishes the regularity of Special Legendrian Cycles, showing they are smooth except at isolated singular points, a significant step in geometric analysis.

Findings

Special Legendrian Cycles are smooth except at isolated points

Links of tangent cones relate to Special Lagrangian currents in Calabi-Yau 3-folds

Provides new insights into the structure of Legendrian cycles in contact geometry

Abstract

Special Legendrian Integral Cycles in $S^5$ are the links of the tangent cones to Special Lagrangian integer multiplicity rectifiable currents in Calabi-Yau 3-folds. We show that such Special Legendrian Cycles are smooth except possibly at isolated points.