Related papers: Results in estimates for $k$-plane transforms
We prove a common generalization to several mass partition results using hyperplane arrangements to split $\mathbb{R}^d$ into two sets. Our main result implies the ham-sandwich theorem, the necklace splitting theorem for two thieves, a…
Jet spaces on $\mathbb R^n$ have been shown to have a canonical structure of stratified Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these…
This is a survey of results on surfaces in noncommutative three-dimensional Lie groups obtained by using the Weierstrass (spinor) representation of surfaces. It is based on the talk given at the conference "Geometry related to the theory of…
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…
We prove an equivariant deformation result for Hamiltonian stationary Lagrangian submanifolds of a Kahler manifold, with respect to deformations of its metric and almost complex structure that are compatible with an isometric Hamiltonian…
New symmetries, norm computations and spectral information are obtained for the Leray transform on a class of unbounded hypersurfaces in $\mathbb{C}^2$. Emphasis is placed on certain distinguished measures, with results on operator norm…
We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representation of the absolute Galois group of K, where K/Q_p is a…
Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of this paper is a…
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
In this paper, we establish compactness results of some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier results obtained by Chang-Ge. In the second part of the paper, as…
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on projective space in any dimension. We also…
The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from…
This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this…
Using an equivariant version of Connes' Thom Isomorphism,w}e prove that equivariant $K$-theory is invariant under strict deformation quantization for a compact Lie group action.
The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…
We show that all the possible pairs of integers occur as exponents for free or nearly free irreducible plane curves and line arrangements, by producing only two types of simple families of examples. The topology of the complements of these…
The inversion theorem for the k-plane Radon transform in R^n is often stated for Schwartz functions, and lately for smooth functions on R^n fulfilling that f(x)=O(|x|^{-N}) for some N>n. In this paper it will be shown, that it suffices to…
We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group $G$…
The number $\nu_{n,d}(k)$ of linearly independed homogeneous invariants of degree $k$ for the $n$-ary form of degree $d$ is calculated.
The subject of these Notes is the new proof, proposed in [F. H{\'e}lein, In{\'e}galit{\'e} isop{\'e}rim{\'e}trique et calibrations, Annales de l'Institut Fourier 44, 4 (1994), 1211-1218] of the classical isoperimetric inequality in the…