Embedding surfaces into $S^3$ with maximum symmetry

Isometric Embedding of Facial Surfaces into S3

The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in threedimensional face recognition treating facial expressions as isometries of the facial surface allows to perform robust recognition insensitive to expressions. Isometry-invariant representation of surfaces ...

Group Actions on Graphs, Maps and Surfaces with Maximum Symmetry

Isometric embedding of Busemann surfaces into L1

In this note, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into L1. As a corollary, we obtain that all planar graphs which are 1skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are L1-embeddable with distortion at most 2 + π/2 < 4. Our results significantly improve and simplify the...

Embedding normed linear spaces into $C(X)$

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

Nanosphere embedding into polymer surfaces: a viscoelastic contact mechanics analysis.

Teichroeb and Forrest [Phys. Rev. Lett. 91, 016104 (2003)] image gold nanosphere embedment into a polystyrene surface and imply the existence of a liquid surface layer. We use a viscoelastic contact mechanics model of their results to give a contrary interpretation. The surface interactions between gold and polystyrene and the indentation depth determine the loads on the nanospheres. Using bulk...