Related papers: Stability of Valuations and Koll\'ar Components

A conjecture of Bombieri states that the coefficients of a normalized univalent function $f$ should satisfy $$ \liminf_{f\to K} \frac{n-{\rm Re\,}a_n}{m-{\rm Re\,}a_m} = \min_{t\in{\mathbb R}} \, \frac{n\sin t -\sin(nt)}{m\sin t -\sin(mt)},…

We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.

Combining the usual energy functional with a higher-order conserved quantity originating from integrability theory, we show that the black soliton is a local minimizer of a quantity that is conserved along the flow of the cubic defocusing…

Let $\gamma_n$ be the standard Gaussian measure on $\mathbb R^n$ and let $(Q_t)$ be the Ornstein--Ulhenbeck semigroup. Eldan and Lee recently established that for every non--negative function $f$ of integral $1$ and any time $t$ the…

We analyze a semi-discrete splitting method for conservation laws driven by a semilinear noise term. Making use of fractional $BV$ estimates, we show that the splitting method produces a compact sequence of approximate solutions converging…

Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base ring of $K$-integers. For every $K$-point…

We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new examples of semistable and unstable singularities. More generally,…

This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…

We generalize Illusie's result to prove the decomposition of the de Rham complex with smooth horizontal coefficients for a semistable $S$-morphism $f:X\ra Y$ which is liftable over $\Z/p^2\Z$. As an application, we prove the Koll\'ar…

We prove singularity criteria for the $t$-K-stability of adjoint foliated structures. We first show that K-semistability of adjoint foliated structures implies log canonicity by extending Odaka's flag ideal characterisation of the mixed…

In this paper, we study the statistical and geometrical properties of the Kullback-Leibler divergence with kernel covariance operators (KKL) introduced by Bach [2022]. Unlike the classical Kullback-Leibler (KL) divergence that involves…

We define a version of stable maps into the classifying stack $B\mathrm{GL}_N$, and develop a corresponding notion of $K$-theoretic Gromov-Witten invariants. In this setting, the evaluation morphisms are not of finite type; the definition…

The single-particle inclusive fragmentation function and the particle multiplicity are observables of fundamental importance in studying properties of quantum chromodynamics at colliders. It is well-known that at high energies, the…

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…

We investigate the K-stability of certain blow-ups of $\mathbb{P}^1$-bundles over a Fano variety $V$, where the $\mathbb{P}^1$-bundle is the projective compactification of a line bundle $L$ proportional to $-K_V$ and the center of the…

Multi-dimensional distributions whose marginal distributions are uniform are called copulas. Among them, the one that satisfies given constraints on expectation and is closest to the independent distribution in the sense of Kullback-Leibler…

Divisorial stability of a polarised variety is a stronger - but conjecturally equivalent - variant of uniform K-stability introduced by Boucksom-Jonsson. Whereas uniform K-stability is defined in terms of test configurations, divisorial…

The paper considers the representation of k-valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k-valued logic are investigated. Theorems are proved on the coincidence of reduced and…

In this paper, we present a general wall crossing theory for K-stability and K-moduli of log Fano pairs whose boundary divisors can be non-proportional to the anti-canonical divisor. Along the way, we prove that there are only finitely many…

This paper proves some results concerning the polar factorisation of an integrable vector-valued function u into the composition of the gradient of a convex function with a measure-preserving mapping. Not every integrable function has a…