Related papers: Singular Yamabe Problem Willmore Energies

As a counterpart of the classical Yamabe problem, a fractional Yamabe flow has been introduced by Jin and Xiong (2014) on the sphere. Here we pursue its study in the context of general compact smooth manifolds with positive fractional…

We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals…

We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a local extension, in the space of…

This paper is a continuation of [TY12] and [QTY13]. We show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore.

We propose and analyze an energy-stable fully discrete parametric approximation for Willmore flow of hypersurfaces in two and three space dimensions. We allow for the presence of spontaneous curvature effects and for open surfaces with…

We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area are uniformly bounded. The analogous energy quantization result holds for Willmore surfaces…

This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" functional $\mathcal{W}$ is considered which involves a…

Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Rr$. We suppose that the mean curvature of the fibers do not change sign. Given a positive differentiable…

We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform…

We study the Yamabe problem on open manifolds of bounded geometry and show that under suitable assumptions there exist Yamabe metrics, i.e. conformal metrics of constant scalar curvature. For that, we use weighted Sobolev embeddings.

We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. We…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

We construct solutions to a Yamabe type problem on a Riemannian manifold M without boundary and of dimension greater than 2, with nonlinearity close to higher critical Sobolev exponents. These solutions concentrate their mass around a non…

In this paper we study the energy function associated to fourth order equations of critical growth on smooth compact conformally flat manifolds of dimension greater or equal than 5.

In this paper, we study the super-Liouville equation with a spinorial Yamabe type term, a natural generalization of Liouville equation, super-Liouville equation and spinorial Yamabe type equation. We establish some refined qualitative…

On conformally compact manifolds we study Yang-Mills equations, their boundary conditions, formal asymptotics, and Dirichlet-to-Neumann maps. We find that smooth solutions with "magnetic" Dirichlet boundary data are obstructed by a…

We present a differential geometric formulation of the Poincare problem using the calculus of moving surfaces (CMS). In this framework, an n dimensional compact hypersurface evolves under a velocity field that couples motion to the…

We discuss the relation between the graded stable derived category of a hypersurface and that of its hyperplane section. The motivation comes from the compatibility between homological mirror symmetry for the Calabi-Yau manifold defined by…

We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…

Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the $m$-sphere, $m\geq2$. Via variational methods, we study analytic aspects…