Finite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy
Sign Up to like & getrecommendations! Published in 2024 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-024-03653-y
Abstract: In this paper we prove that the space M(n,v,D,Λ):={(Mn,g)closed:Ric≥-(n-1),Vol(M)≥v>0,diam(M)≤Dand∫M|Rm|n/2≤Λ}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}(n,\textrm{v},D,\Lambda ):=\{(M^n,g) \text { closed }: ~~\textrm{Ric}\ge -(n-1),~\textrm{Vol}(M)\ge \textrm{v}>0, \text {diam}(M)\le D \text { and } \int… read more here.
Keywords: diffeomorphism; documentclass 12pt; document; usepackage ... See more keywords
A Global Diffeomorphism Theorem for Fréchet Spaces
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DOI: 10.1007/s10958-020-04802-4
Abstract: We establish sufficient conditions for a C c 1 $$ {C}_c^1 $$ -local diffeomorphism between Fréchet spaces to be a global diffeomorphism. We extend Clarke’s theory of generalized gradients to more general Fréchet spaces. As… read more here.
Keywords: global diffeomorphism; diffeomorphism; spaces global; theorem ... See more keywords
Game-Theoretic Optimization Toward Diffeomorphism-Based Robust Control of Fuzzy Dynamical Systems With State and Input Constraints
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DOI: 10.1109/tfuzz.2023.3298341
Abstract: This work investigates a game-theoretic optimization approach toward robust control of uncertain dynamical systems with state and input constraints. The uncertainty involved is possibly rapidly time-varying but bounded within a prescribed fuzzy set. For this,… read more here.
Keywords: system; diffeomorphism; control; state ... See more keywords
Scenario of stable transition from diffeomorphism of torus isotopic to identity one to skew product of rough transformations of circle
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DOI: 10.13108/2024-16-1-10
Abstract: In this paper, we consider gradient-like diffeomorphisms of a two-dimensional torus isotopic to the identical one. The isotopicity of diffeomorphisms $f_0$, $f_1$ on an $n$-manifold $M^n$ means the existence of some arc $\{f_t:M^n\to M^n,t\in[0,1]\}$ connecting… read more here.
Keywords: torus isotopic; diffeomorphism; torus; rough transformations ... See more keywords
Controllability and diffeomorphism groups on manifolds with boundary
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DOI: 10.1515/forum-2024-0160
Abstract: Abstract In this article we consider diffeomorphism groups of manifolds with smooth boundary. We show that the diffeomorphism groups of the manifold and its boundary fit into a short exact sequence which admits local sections.… read more here.
Keywords: groups manifolds; diffeomorphism; diffeomorphism groups; manifolds boundary ... See more keywords