A convexity theorem for Poisson actions of compact Lie groups
A coordinatewise formulation of geometric quantization
A correction to "A note on equichordal graphs" (Port. Math., 45(4) (1988), 363-368)
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A counterexample to the rigidity conjecture for polyhedra
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...
A curvature identity on a 6-dimensional Riemannian manifold and its applications
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a...
A. D. Alexandrov's length manifolds with one-sided bounded curvature
A. D. Alexandrov's problem for -spaces.
A. D. Alexandrov's uniqueness theorem for convex polytopes and its refinements.
A description of derivations of the algebra of symmetric tensors
In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.
A diameter sphere theorem for mainfolds of positive Ricci curvature.
A differential geometric characterization of invariant domains of holomorphy
Let be a complex reductive group. We give a description both of domains and plurisubharmonic functions, which are invariant by the compact group, , acting on by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space . Such an invariant domain with a smooth boundary is Stein if and only if the corresponding domain is geodesically convex and the sectional curvature of its boundary fulfills the condition . The term is explicitly computable...
A differential geometric characterization of symmetric spaces of higher rank
A Direct Approach to the Determination of Gaussian and Scalar Curvature Functions.
A Direct Extension Method for CR Structures.
A direct method approach for the existence of convex hypersurfaces with prescribed Gauss-Kronecker curvature.
A Dirichlet problem for an H-system with variable H.
A discrete version of the Brunn-Minkowski inequality and its stability
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for metric measure spaces. Our new definition, based only on properties of the distance, allows also us to deal with discrete metric measure spaces. Then we show the stability of our new inequality under convergence of metric measure spaces. This result gives as corollary the stability of the classical Brunn-Minkowski inequality for geodesic spaces. The proof of this stability...
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.