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Title: Rigidity of Polyhedral surfaces
Abstract: Classical differential geometry deals with smooth surfaces and
Riemannian metrics. In contrast, a polyhedral surface, such as a tetrahedron,
is a surface composed of Euclidean (or spherical, hyperbolic) triangles.
This talk discusses the geometry of polyhedral surfaces. One of the main
problems on surface geometry is to understand the relationship between
curvature and metric. The metric-curvature relation for polyhedral surfaces
is governed by the cosine law. We will show you how derivative of the cosine
law implies many rigidity phenomena about the polyhedral surfaces. Applications
to the Teichmuller space of surfaces with boundary will also be discussed. |