# Willmore and Generalized Willmore energies in space forms

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## Abstract

This PhD dissertation consists of two sections. In the first part of this work, we study a Generalized Willmore flow equation
and its numerical applications. First, we derive the time dependent equation
which relates to the geometric evolution of a Generalized Willmore flow on a general
immersion. Then, we transform this equation into a coupled system of second order nonlinear
PDEs together with the mean curvature formula on a general immersion in

In the second part, we study Willmore-type energies and Willmore-type immersions in space forms. In fact,
we introduce the notion of deformed Willmore energy for a space form

\item determining the natural choices of the constant