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Award ID contains: 2054593

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  1. ; ; (, Proceedings of the London Mathematical Society)
    Abstract We obtain optimal estimates of the Poincaré constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincaré constant is determined by thesecondlargest end. The proof is based on the argument by Kusuoka–Stroock where the heat kernel estimates on the central balls play an essential role. For this purpose, we extend earlier heat kernel estimates obtained by the authors to a larger class of parabolic manifolds with ends. 
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  2. ; (, Mathematische Nachrichten)
    Abstract This paper aims at proving the local boundedness and continuity of solutions of the heat equation in the context of Dirichlet spaces under some rather weak additional assumptions. We consider symmetric local regular Dirichlet forms, which satisfy mild assumptions concerning (1) the existence of cut‐off functions, (2) a local ultracontractivity hypothesis, and (3) a weak off‐diagonal upper bound. In this setting, local weak solutions of the heat equation, and their time derivatives, are shown to be locally bounded; they are further locally continuous, if the semigroup admits a locally continuous density function. Applications of the results are provided including discussions on the existence of locally bounded heat kernel; structure results for ancient (local weak) solutions of the heat equation. 
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  3. ; (, Stochastic Processes and their Applications)
    Free, publicly-accessible full text available July 1, 2026
  4. ; (, Pure and Applied Functional Analysis)
    Accepted Manuscript Full Text Available
  5. ; (, Potential Analysis)
    Full Text Available 
  6. ; (, Electronic Journal of Probability)
    Full Text Available 
  7. (, EMS Press)
    Full Text Available 
  8. ; (, Journal of Differential Equations)
    Full Text Available 
  9. ; ; ; ; (, Springer)
    This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups. 
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    Accepted Manuscript Full Text Available
  10. ; (, Electronic Journal of Probability)
    Full Text Available