The shape of a figure-eight under the curve shortening flow.
The sharp isoperimetric inequality for minimal surfaces with radially connectred boundary in hyperbolic space.
The short-time propagator and the boundary conditions in the quantum mechanics
The single screw reciprocal to the general plane-symmetric six-screw linkage.
The singularities of Yang-Mills connections for bundles on a surface.
The Singularity of the Canonical Model of Compact Kähler Manifolds.
The singularity structureοf the Yang-Mills configuration space
The geometric description of Yang–Mills theories and their configuration space is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analysed in detail for structure group SU(2). This review is based on [28].
The size of the shadow boundary pojection.
The Soliton-Ricci Flow with variable volume forms
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation. This gauge is generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times. It represents the gradient flow of...
The space of clouds in Euclidean space.
The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature.
The spacetime positive mass theorem in dimensions less than eight
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality holds, where is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem...
The spectra and the symmetric structure on a compact symmetric space.
The spectral geometry of the Weyl conformal tensor
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.
The spectrum of the -Laplacian on Kähler manifolds
The Spectrum of the Bochner-Laplace Operator on the 1-Forms on a Compact Riemannian Manifold.
The spectrum of the Laplace operator for a spherical space form
Si determina lo spettro di un operatore di Laplace di una «spherical space form» e si studia l’influenza di tale spettro su .
The spectrum of the Laplace operator on conformally flat manifolds
The spherical transform for homogeneous vector bundles over Riemannian symmetric spaces.
The spray and antispray theory in the subspaces of Miron's .