Publications [#345592] of Mark Haskins

Papers Published

1. Haskins, M; Kapouleas, N, The geometry of SO(p) × SO(q)-invariant special Lagrangian cones, Communications in Analysis and Geometry, vol. 21 no. 1 (January, 2013), pp. 171-205 [doi]
   (last updated on 2026/01/16)

   Abstract:
   SO(p) × SO(q)-invariant special Lagrangian cones in ℂ^p+q(equivalently, SO(p) × SO(q)-invariant special Legendrians in S^2(p+q)-1) are an important family of special Lagrangians (SL) whose basic features were studied in our previous paper [13]. In some ways, they play a role analogous to that of Delaunay surfaces in the geometry of CMC surfaces in ℝ³; in particular, they are natural building blocks for our gluing constructions of higher-dimensional SL cones [9, 10, 12]. In this article, we study in detail their geometry paying special attention to features needed in our gluing constructions. In particular, we classify them up to congruence; we determine their full group of symmetries (including various discrete symmetries) in all cases; we prove that many of them are closed and embedded; and finally understand the limiting singular geometry with detailed asymptotics. In understanding the detailed asymptotics a fundamental role is played by a certain conserved quantity (a component of the torque) considered in [13].