| This document records three distinct theorems that the author proved, along with his collaborators, while a graduate student at The Johns Hopkins University. The author, with M. Calle and J. Kramer, generalized a sharp estimate of Tobias Colding and William Minicozzi for the extinction time of convex hyper-surfaces in euclidean space moving by their mean curvature vector to a much broader class of evolutions studied by Ben Andrews in (1). Also, the author gave an alternate proof, first given by D. Hoffman and B. White in (17), of very poor limiting behavior for sequences of minimal surfaces in euclidean three space. Finally, the author, together with N. Moller in (23) constructed a new family of asymptotically conical ends that satisfy the mean curvature self shrinking equation in euclidean three space in all dimensions. |
