Singularities of flat extensions from generic surfaces with boundaries
Goo Ishikawa
TL;DR
This paper investigates the singularities arising in flat extensions of generic surfaces with boundaries in 3D space, linking boundary singularities to envelope theory and duality principles.
Contribution
It introduces a novel analysis of boundary singularities in flat extensions and explores duality in Legendre surfaces with boundaries, providing new formulae for remote boundary-envelope singularities.
Findings
Relation between boundary singularities and envelope theory
Duality principles in boundary singularities of Legendre surfaces
Explicit formulae for remote boundary-envelope singularities
Abstract
We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries via projective duality and observe the duality on boundary singularities. Moreover we give formulae related to remote singularities of the boundary-envelope.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Geometric and Algebraic Topology