Analytisch-geometrische Untersuchungen.
Anisotropic geometric functionals and gradient flows
We survey some recent results on the gradient flow of an anisotropic surface energy, the integrand of which is one-homogeneous in the normal vector. We discuss the reasons for assuming convexity of the anisotropy, and we review some known results in the smooth, mixed and crystalline case. In particular, we recall the notion of calibrability and the related facet-breaking phenomenon. Minimal barriers as weak solutions to the gradient flow in case of nonsmooth anisotropies are proposed. Furthermore,...
Anosov flows and non-Stein symplectic manifolds
We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of...
Anti-invariant Riemannian submersions from almost Hermitian manifolds
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold...
Anti-Invariant Submanifolds of Almost Contact Metric Manifolds.
Anti-self-dual Hermitian metrics on blown-up Hopf surfaces.
Anti-self-dual orbifolds with cyclic quotient singularities
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...
Anwendungen der differentialtopologischen Berechnung der totalen Krümmung und totalen Absolutkrümmung in der sphärischen Differentialgeometrie.
Any Hermitian Metric of Constant Non-Positive (Hermitian) Holomorphic Sectional Curvature on a Compact Complex Surface is Kähler.
Appendice : « Décomposition en produit de deux browniens d'une martingale à valeurs dans un groupe muni d'une métrique bi-invariante »
Appendix (to D. McDuff and L. Polterovich)
Applications Harmoniques de Variétés Produits.
Applications of Lie derivatives to symmetries, geodesic mappings, and first integrals in Riemannian spaces
Applications of spectral geometry to affine and projective geometry.
Applications of symplectic homology II: Stability of the action spectrum.
Applications of the group analysis of differential equations to some systems of noncommuting -smooth vector fields.
Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian
We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.
Applications of the Kähler-Einstein-Calabi-Yau Metric to Moduli of K3 Surfaces.
Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds
To any smooth compact manifold endowed with a contact structure and partially integrable almost CR structure , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric on . We consider the asymptotic expansion, in powers of a special defining function, of the volume of with respect to and prove that the log term coefficient is independent of (and any choice of contact...
Approximation by positive mean curvature immersions: frizzing.