Double bubbles with high constant mean curvatures in Riemannian manifolds

@article{Matteo2021DoubleBW,
  title={Double bubbles with high constant mean curvatures in Riemannian manifolds},
  author={Gianmichele Di Matteo and Andrea Malchiodi},
  journal={Nonlinear Analysis},
  year={2021}
}

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References

SHOWING 1-10 OF 48 REFERENCES

Constant mean curvature spheres in Riemannian manifolds

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

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

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

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

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

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

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

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

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

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