Some New Results in Geometric Analysis

Abstract

This thesis presents three results in geometric analysis. We first analyze the curve-shortening flow on figure eight curves in the plane. Afterwards, we examine the point-wise curvature preserving flow on space curves. Lastly, we present an abridgment of our work on a family of three-dimensional Lie groups, which, when equipped with canonical left-invariant metrics, interpolate between Sol and hyperbolic space.

Undergraduate thesis, Brown University, 72 pages. Further clarifications made in Chapter 2. arXiv admin note: text overlap with arXiv:2005.06430

References in corpus (4)

• Families of Geometries, Real Algebras, and Transitions
• An Interpolation from Sol to Hyperbolic Space
• On Area Growth in Sol
• Stationary Solutions of the Curvature Preserving Flow on Space Curves