Related papers: The critical space for orthogonally invariant vari…
We prove multiplicity theorems for Keller $ C_c^1 $-functionals on Frechet spaces and Finsler manifolds which are invariant under the action of a discrete subgroup. For such functionals, we evaluate the minimal number of critical points by…
We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions with anticommuting scalars transforming under the symplectic group $\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all operator…
In the first part of this paper we study a best approximation of a vector in Euclidean space R^n with respect to a closed semi-algebraic set C and a given semi-algebraic norm. Assuming that the given norm and its dual norm are…
Utilizing a new variational principle that allows dealing with problems beyond the usual locally compactness structure, we study problems with a supercritical nonlinearity of the type $ -\Delta u + u= a(x) f(u)$ in $ \Omega$ with…
In both quantum computing and black hole physics, it is natural to regard some deformations, infinitesimal unitaries, as \emph{easy} and others as \emph{hard}. This has lead to a renewed examination of right-invariant metrics on…
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…
The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations…
Let $G$ be one of the classical compact, simple, centre-less, connected Lie groups or rank $n$ with a maximal torus $T$, the Lie algebra $\clg$ and let $\{ E_i, F_i, H_i, i=1, \ldots, n \}$ be the standard set of generators corresponding to…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
Let $\{T(t)\}_{t\geq0}$ be a $C_0$-semigroup on an infinite dimensional separable Hilbert space; a suitable definition of near $\{T(t)^*\}_{t\geq0}$ invariance of a subspace is presented in this paper. A series of prototypical examples for…
For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n}…
A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…
In this paper, we study the symmetry properties of nondegenerate critical points of shape functionals using the implicit function theorem. We show that, if a shape functional is invariant with respect to some continuous group of rotations,…
The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value…
Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$,…
We study critical points of holomorphic sections of $\ocal(m)$ on $\CP^n$. For quadrics, we give a complete discription of their critical points. When $n=1$, we prove a spherical Gauss-Lucas theorem. For general situation, we prove that a…
Let $f$ be an entire transcendental function of finite order and $\Delta$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class $\mathcal{H}$. We show that if $f$ has two singular values with bounded…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in…
Given discrete groups $\Gamma \subset \Delta$ we characterize $(\Gamma,\sigma)$-invariant spaces that are also invariant under $\Delta$. This will be done in terms of subspaces that we define using an appropriate Zak transform and a…