New examples of translating solitons fully nonlinear extrinsic geometric flows and their consequences.
Document Type
Event
Faculty Mentor
José Torres
Abstract
Geometric flows describe how shapes evolve under curvature-dependent rules, often developing singularities that reveal important geometric and analytical structures. This talk introduces the study of extrinsic geometric flows—those defined by the embedding of a hypersurface in ambient space—with a special emphasis on self-similar translational solutions. These self-similar motions, which evolve by rigid translation, serve as models for certain singular behaviors that naturally arise in curvature-driven flows. I will present recent work on constructing catenoidal-type translating solutions for a broad class of curvature flows defined by symmetric functions of the principal curvatures and discuss their geometric features and analytical applications.
New examples of translating solitons fully nonlinear extrinsic geometric flows and their consequences.
Geometric flows describe how shapes evolve under curvature-dependent rules, often developing singularities that reveal important geometric and analytical structures. This talk introduces the study of extrinsic geometric flows—those defined by the embedding of a hypersurface in ambient space—with a special emphasis on self-similar translational solutions. These self-similar motions, which evolve by rigid translation, serve as models for certain singular behaviors that naturally arise in curvature-driven flows. I will present recent work on constructing catenoidal-type translating solutions for a broad class of curvature flows defined by symmetric functions of the principal curvatures and discuss their geometric features and analytical applications.
