Free boundary minimal surfaces with connected boundary and arbitrary genus

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions

On a free boundary problem and minimal surfaces

From minimal surfaces such as Simons’ cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that Savin’s theorem [43] is optimal.

Analysis of Free Vibration of Triangular Plates with Non-Uniform Linear Thickness and Arbitrary Boundary Conditions

Minimal Surfaces with Planar Boundary Curves

In 1956, Shiffman [Sh] proved that any compact minimal annulus with two convex boundary curves (resp. circles) in parallel planes is foliated by convex planar curves (resp. circles) in the intermediate planes. In 1978, Meeks conjectured that the assumption the minimal surface is an annulus is unnecessary [M]; that is, he conjectured that any compact connected minimal surface with two planar con...

Bending Analysis of Laminated Composite Plates with Arbitrary Boundary Conditions

It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with ar...