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4 papers
Local space time constant mean curvature and constant expansion foliations
Jan Metzger, Alejandro Peñuela Diaz
Inspired by the small sphere-limit for quasi-local energy we study local foliations of surfaces with prescribed mean curvature. Following the strategy used by Ye in 1991 to study l…
Isoperimetry in Surfaces of Revolution with Density
Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar +1
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-co…
The Least-Area Tetrahedral Tile of Space
Eliot Bongiovanni, Alejandro Diaz, Arjun Kakkar +1
We determine the least-area unit-volume tetrahedral tile of Euclidean space, without the constraint of Gallagher et al. that the tiling uses only orientation-preserving images of t…
Double Bubbles on the Real Line with Log-Convex Density
Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz +6
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in is the standard double bubble. We seek the opti…