## One Citation

### Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds

- Mathematics
- 2022

. We prove the existence of multiple solutions to the Allen–Cahn–Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small volume constraint on…

## References

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### Constant mean curvature spheres in Riemannian manifolds

- Mathematics
- 2009

We prove the existence of embedded spheres with large constant mean curvature in any compact Riemannian manifold (M, g). This result partially generalizes a result of R. Ye which handles the case…

### The isoperimetric profile of a smooth Riemannian manifold for small volumes

- Mathematics
- 2009

We define a new class of submanifolds called pseudo-bubbles, defined by an equation weaker than constancy of mean curvature. We show that in a neighborhood of each point of a Riemannian manifold,…

### Foliation by constant mean curvature spheres

- Mathematics
- 1991

Let M be a Riemannian manifold of dimension n+l and p e M. Geodesic spheres around p of small radius constitute a smooth foliation. We shall show that this foliation can be perturbed into a foliation…

### Small Surfaces of Willmore Type in Riemannian Manifolds

- Mathematics
- 2009

In this paper we investigate the properties of small surfaces of Willmore type in Riemannian manifolds. By small surfaces we mean topological spheres contained in a geodesic ball of small enough…

### Some Sharp Isoperimetric Theorems for Riemannian Manifolds

- Mathematics
- 2000

We prove that a region of small prescribed volume in a smooth, compact Riemannian manifold has at least as much perimeter as a round ball in the model space form, using dif- ferential inequalities…

### Area-minimizing regions with small volume in Riemannian manifolds with boundary

- Mathematics
- 2009

Given a domain Ω of a Riemannian manifold, we prove that regions minimizing the area (relative to Ω) are nearly the maxima of the mean curvature of ∂Ω when their volume tends to zero. We deduce some…

### Improved convergence theorems for bubble clusters. I. The planar case

- Mathematics
- 2014

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified…

### Embedded area‐constrained Willmore tori of small area in Riemannian three‐manifolds I: minimization

- Mathematics
- 2014

We construct embedded Willmore tori with small area constraint in Riemannian three‐manifolds under some curvature condition used to prevent Möbius degeneration. The construction relies on a…

### Local foliation of manifolds by surfaces of Willmore type

- Mathematics
- 2018

We show the existence of a local foliation of a three dimensional Riemannian manifold by critical points of the Willmore functional subject to a small area constraint around non-degenerate critical…

### Concentration of CMC Surfaces in a 3-manifold

- Mathematics
- 2012

We prove that simply connected H-surfaces with small diameter in a 3-manifold necessarily concentrate at a critical point of the scalar curvature. Introduction Let (N, g) be a compact oriented…