اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTwo dimensional Berezin-Li-Yau inequalities with a correction term
38
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas.
قيم البحث
اقرأ أيضاً
We give an improvement of sharp Berezin type bounds on the Riesz means $sum_k(Lambda-lambda_k)_+^sigma$ of the eigenvalues $lambda_k$ of the Dirichlet Laplacian in a domain if $sigmageq 3/2$. It contains a correction term of the order of the standard
second term in the Weyl asymptotics. The result is based on an application of sharp Lieb-Thirring inequalities with operator valued potential to spectral estimates of the Dirichlet Laplacian in domains.
In this paper we study the eigenvalue sums of Dirichlet Laplacians on bounded domains. Among our results we establish an improvement of the Li-Yau bound in the presence of a constant magnetic field.
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $R^d$, $d geq 2$. In particular, we derive upper bounds on Riesz means of order $sigma geq 3/2$, that improve the sharp Berezin inequality by a negative s
econd term. This remainder term depends on geometric properties of the boundary of the set and reflects the correct order of growth in the semi-classical limit. Under certain geometric conditions these results imply new lower bounds on individual eigenvalues, which improve the Li-Yau inequality.
We consider a Schrodinger operator on the half-line with a Dirichlet boundary condition at the origin and show that moments of its negative eigenvalues can be estimated by the part of the potential that is larger than the critical Hardy weight. The e
stimate is valid for the critical value of the moment parameter.
In recent papers Wu-Yau, Tosatti-Yang and Diverio-Trapani, used some natural differential inequalities for compact Kahler manifolds with quasi negative holomorphic sectional curvature to derive positivity of the canonical bundle. In this note we study the equality case of these inequalities.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
