Related papers: Remarks on logarithmic K-stability
We perform some simulations of the semilinear Klein--Gordon equation with a power-law nonlinear term and propose each of the quantitative evaluation methods for the stability and convergence of numerical solutions. We also investigate each…
This note is a commentary on the model-theoretic interpretation of Grothendieck's double limit characterization of weak relative compactness.
We survey some recent development in the stability theory of klt singularities. The main focus is on the solution of the stable degeneration conjecture.
In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…
We compute K-semistable domains for various examples of log pairs.
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…
In this paper, we make a generalization of the results in \cite{Li22a} to the singular and weighted setting. In particular, we show that on a polarized projective klt variety, the $\mathbb{G}$-uniform weighted K-stability for models implies…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
K-polystability of a polarised variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature K\"ahler metric. When a variety is K-unstable, it is expected to admit a "most destabilising"…
This survey is mostly concerned with unstable analogues of the Lichtenbaum-Quillen Conjecture. The Lichtenbaum-Quillen Conjecture (now implied by the Voevodsky-Rost Theorem) attempts to describe the algebraic K-theory of rings of integers…
In this paper we present a proof of the orbital stability of ground state for logarithmic Schr\"odinger equation in any dimension and under nonradial perturbations.
In this note, we prove that on polarized toric manifolds the relative $K$-stability with respect to Donaldson's toric degenerations is a necessary condition for the existence of Calabi's extremal metrics, and also we show that the modified…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying…
We use $G$-stable pieces to construct some equidimensional varieties and as a consequence, obtain Lusztig's dimension estimates \cite[section 4]{L2}. This is a generalization of \cite{HL}.
We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the authors established the well-posedness and…
The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.