Sharp estimate on the inner distance in planar domains
نویسندگان
چکیده
منابع مشابه
Sharp bounds for the p-torsion of convex planar domains
We obtain some sharp estimates for the p-torsion of convex planar domains in terms of their area, perimeter, and inradius. The approach we adopt relies on the use of web functions (i.e. functions depending only on the distance from the boundary), and on the behaviour of the inner parallel sets of convex polygons. As an application of our isoperimetric inequalities, we consider the shape optimiz...
متن کاملPractical Distance Functions for Path-Planning in Planar Domains
Path planning is an important problem in robotics. One way to plan a path between two points x, y within a (not necessarily simply-connected) planar domain Ω, is to define a non-negative distance function d(x, y) on Ω × Ω such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge – to defin...
متن کاملthe impact of e-readiness on ec success in public sector in iran the impact of e-readiness on ec success in public sector in iran
acknowledge the importance of e-commerce to their countries and to survival of their businesses and in creating and encouraging an atmosphere for the wide adoption and success of e-commerce in the long term. the investment for implementing e-commerce in the public sector is one of the areas which is focused in government‘s action plan for cross-disciplinary it development and e-readiness in go...
On the Inner Radius of Nodal Domains
Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λα(log λ)β . Our proof is based on a local behavior of eigenfunctions discovered by Donnelly and Fefferman and a Poincaré type inequality proved by Maz’ya. Sharp lower bounds are known only in dimension two. We give an a...
متن کاملSharp Spectral Bounds on Starlike Domains
We prove sharp bounds on eigenvalues of the Laplacian that complement the Faber–Krahn and Luttinger inequalities. In particular, we prove that the ball maximizes the first eigenvalue and minimizes the spectral zeta function and heat trace. The normalization on the domain incorporates volume and a computable geometric factor that measures the deviation of the domain from roundness, in terms of m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2020
ISSN: 0004-2080,1871-2487
DOI: 10.4310/arkiv.2020.v58.n1.a9