Comparison of Exit Moment Spectra for Extrinsic Metric Balls

Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente

doi:10.1007/s11118-011-9223-3

Cited by 11 publications

(27 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We should also mention that the case p = 1 is naturally of special interest, and has produced a literature too large to describe here; the case of general p has attracted somewhat less interest, nevertheless the reader interested in other results relating the p-th moments of Brownian exit time with the geometry of domains is referred to [1,4,7,9,10,13,14,15,16,20,21,22,23,27,28].…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

On the finiteness of moments of the exit time of planar Brownian motion from comb domains

Boudabra

Markowsky

2021

Ann. Fenn. Math.

View full text Add to dashboard Cite

A comb domain is defined to be the entire complex plain with a collection of vertical slits, symmetric over the real axis, removed. In this paper, we consider the question of determining whether the exit time of planar Brownian motion from such a domain has finite p-th moment. This question has been addressed before in relation to starlike domains, but these previous results do not apply to comb domains. Our main result is a sufficient condition on the location of the slits which ensures that the p-th moment of the exit time is finite. Several auxiliary results are also presented, including a construction of a comb domain whose exit time has infinite p-th moment for all p ≥ 1/2.

show abstract

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

On the finiteness of moments of the exit time of planar Brownian motion from comb domains

Boudabra

Markowsky

2021

Ann. Fenn. Math.

View full text Add to dashboard Cite

show abstract

“…. } have been studied in several papers ( [10,11,17,18,20,21]). We point out that T 1 ( ) has also an intepretation in mechanics, being the torsional rigidity of the domain ; isoperimetric inequalities for the functional T 1 ( ) are classical, and were recently extended to the higher exit time moments.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…is known as the exit time moment spectrum of . These invariants have been studied in the papers [10,11,17,18,20,21].…”

Section: Exit Time Momentsmentioning

confidence: 99%

“…These identities show the strict relation between the exit time moments and the heat content. The relation between the moment spectrum and the Dirichlet spectrum has been studied in [10,11] and [17].…”

Section: Exit Time Momentsmentioning

confidence: 99%

“…On the other hand, for all s ∈ (0, t) one has that ∂v ∂ N (s, y) converges to ∂u ∂ N (s, y) (from below, see (17)). Therefore, by the dominated convergence theorem, we conclude:…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 2 more Smart Citations

On the heat content functional and its critical domains

Savo

2021

Calc. Var.

View full text Add to dashboard Cite

We study and classify smooth bounded domains in an analytic Riemannian manifold which are critical for the heat content at all times $$t>0$$ t > 0 . We do that by first computing the first variation of the heat content, and then showing that $$\Omega $$ Ω is critical if and only if it has the so-called constant flow property, so that we can use a previous classification result established in [33] and [34]. The outcome is that $$\Omega $$ Ω is critical for the heat content at time t, for all $$t>0$$ t > 0 , if and only if $$\Omega $$ Ω admits an isoparametric foliation, that is, a foliation whose leaves are all parallel to the boundary and have constant mean curvature. Then, we consider the sequence of functionals given by the exit-time moments $$T_1(\Omega ),T_2(\Omega ),\dots $$ T 1 ( Ω ) , T 2 ( Ω ) , ⋯ , which generalize the torsional rigidity $$T_1$$ T 1 . We prove that $$\Omega $$ Ω is critical for all $$T_k$$ T k if and only if $$\Omega $$ Ω is critical for the heat content at every time t, and then we get a classification as well. The main purpose of the paper is to understand the variational properties of general isoparametric foliations and their role in PDE’s theory; in some respects they generalize the properties of the foliation of $$\mathbf{R}^{n}$$ R n by Euclidean spheres.

show abstract

First Dirichlet Eigenvalue and Exit Time Moments: A Survey

Gimeno,

Hurtado

2023

New Trends in Geometric Analysis

View full text Add to dashboard Cite

Comparison of Exit Moment Spectra for Extrinsic Metric Balls

Cited by 11 publications

References 28 publications

On the finiteness of moments of the exit time of planar Brownian motion from comb domains

On the finiteness of moments of the exit time of planar Brownian motion from comb domains

On the heat content functional and its critical domains

First Dirichlet Eigenvalue and Exit Time Moments: A Survey

Contact Info

Product

Resources

About