We construct closed embedded minimal surfaces in the round three-sphere $\mathbb {S}^ 3
(1) $, resembling two parallel copies of the equatorial two-sphere $\mathbb {S}^ 2_ {\mathrm …

One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on
calibrations in semi-riemannian geometry where split SLAG geometry was first introduced …

Associative submanifolds of the 7-sphere 𝒮7 are 3-dimensional minimal submanifolds
which are the links of calibrated 4-dimensional cones in ℝ8 called Cayley cones. Examples …

In this paper we refine the construction and related estimates for complete constant mean
curvature surfaces in Euclidean three-space developed in Kapouleas (Ann Math 131: 239 …

In this article we provide a general construction when $ n\ge3 $ for immersed in Euclidean
$(n+ 1) $-space, complete, smooth, constant mean curvature hypersurfaces of finite …

The paper studies how to extend local calibration pairs to global ones in various situations.
As a result, new discoveries involving mass-minimizing properties are exhibited. In …

We describe several families of Lagrangian submanifolds in complex Euclidean space
which are H-minimal, ie critical points of the volume functional restricted to Hamiltonian …

Plateau's problem was raised by Joseph-Louis Lagrange in 1760 and later named after
Joseph Plateau who did many interesting experiments using soap films. Over the past 90 …

This is a contribution to a special volume in honor of Professor R. Schoen for his sixtieth
birthday. In the article, I introduce and survey some developments related to the metric …