@article {RIZZI20175306,
	title = {Clifford Tori and the singularly perturbed Cahn{\textendash}Hilliard equation},
	journal = {Journal of Differential Equations},
	volume = {262},
	number = {10},
	year = {2017},
	pages = {5306 - 5362},
	abstract = {<p>In this paper we construct entire solutions uε to the Cahn{\textendash}Hilliard equation -ε2Δ(-ε2Δu+W'(u))+W"(u)(-ε2Δu+W'(u))=ε4λε(1-uε), under the volume constraint ∫R3(1-uε)2dx=82π2cε, with cε{\textrightarrow}1 as ε{\textrightarrow}0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε{\textrightarrow}0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov{\textendash}Schmidt reduction and on careful geometric expansions of the Laplacian.</p>},
	keywords = {Cahn{\textendash}Hilliard equation, Clifford Torus, Lyapunov{\textendash}Schmidt reduction, Willmore surface},
	issn = {0022-0396},
	doi = {https://doi.org/10.1016/j.jde.2017.01.026},
	url = {http://www.sciencedirect.com/science/article/pii/S0022039617300530},
	author = {Matteo Rizzi}
}
@article {rizzi2016critical,
	title = {Critical points of a perturbed Otha-Kawasaki functional},
	journal = {arXiv preprint arXiv:1601.07093},
	year = {2016},
	author = {Matteo Rizzi}
}
