Related papers: On Weighted Twisted K-Energy and Its Applications

A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…

Let $(X,\omega)$ be a compact K\"ahler manifold and $\mathcal H$ the space of K\"ahler metrics cohomologous to $\omega$. If a cscK metric exists in $\mathcal H$, we show that all finite energy minimizers of the extended K-energy are smooth…

An explicit seminorm $||f||_{#}$ on the vector space of Chow vectors of projective varieties is introduced, and shown to be a generalized Mabuchi energy functional for Chow varieties. The singularities of the Chow varieties give rise to…

Consider a compact surface of genus $\geq 2$ equipped with a metric that is flat everywhere except at finitely many cone points with angles greater than $2\pi$. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson,…

We explore probabilistic approaches to the deterministic energy equality for the forced Surface Quasi-Geostrophic (SQG) equation on a torus. First, we prove the zero-noise dynamical large deviations for a corresponding stochastic SQG…

Adiabatic and inviscid axisymmetric perturbations to a stable reference vortex in gradient wind balance are known to experience two kinds of restoring forces: one that is proportional to both the perturbation density and the reference…

In this paper, we study the stability of the conical K\"ahler-Ricci flows on Fano manifolds. That is, if there exists a conical K\"ahler-Einstein metric with cone angle $2\pi\beta$ along the divisor, then for any $\beta'$ sufficiently close…

We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the…

We proceed further with the study of minimum weak Riesz energy problems for condensers with touching plates, initiated jointly with Bent Fuglede (Potential Anal. 51 (2019), 197--217). Having now added to the analysis constraint and external…

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…

We use the correspondence between extremal Sasaki structures and weighted extremal Kahler metrics defined on a regular quotient of a Sasaki manifold, established by the first two authors, and Lahdili's theory of weighted K-stability in…

In this paper, we introduce a class of Sasaki manifolds with a reductive $G$-group action, called $G$-Sasaki manifolds. By reducing K-energy to a functional defined on a class of convex functions on a moment polytope, we give a criterion…

The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Zamfirescu and T-weak contraction mappings in the framework of complete cone metric spaces.

We investigate the inertial limit of the compressible Navier--Stokes system posed on the $3$-dimensional torus, and allowing for regions of vacuum. Considering global-in-time finite-energy weak solutions of a scaled system, we rigorously…

We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean…

This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth…

It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the…

Let $\mu$ be a Radon measure on $\mathbb{R}^d$. We define and study conical energies $\mathcal{E}_{\mu,p}(x,V,\alpha)$, which quantify the portion of $\mu$ lying in the cone with vertex $x\in\mathbb{R}^d$, direction $V\in G(d,d-n)$, and…

In the setting of electromagnetic systems, we propose a new definition of electromagnetic Ricci curvature, naturally derived via the classical Jacobi-Maupertuis reparametrization from the recent works of Assenza [IMRN, 2024] and Assenza,…

Let $(X,\omega)$ be a compact K\"ahler manifold. We prove the existence and uniqueness of solutions to complex Monge-Amp\`ere equations with prescribed singularity type. Compared to previous work, the assumption of small unbounded locus is…