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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

12 votes
0 answers
395 views

A model of pillows

(The same system with slightly different questions has been asked in MSE.) Let $\Omega\subset \mathbb{R}^2$ be some simply connected planar domain. We seek for a mapping $\mathbf{r}:\Omega\rightarrow …
Daniel Castro's user avatar
3 votes
2 answers
221 views

$2\mathrm{d}$ area maximizing short embeddings

Think of a beach ball on an pool of water or sand. Let $\left(\mathcal{M}^2,g\right)$ be a surface homeomorphic to a sphere, endowed with a Riemannian metric $g$, and $\left(\mathcal{N}^2,h\right)$ a …
Daniel Castro's user avatar