Weakly non-collapsed RCD spaces are strongly non-collapsed
نویسندگان
چکیده
Abstract We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms conjecture raised by De Philippis and second named author in full generality. One auxiliary results independent interest we obtain about link between properties tr ? ( Hess f stretchy="false">) = ? ? \operatorname{tr}(\operatorname{Hess}f)=\Delta f on U ? mathvariant="sans-serif">X U\subseteq{\mathsf{X}} for every ???? sufficiently regular, mathvariant="fraktur">m c mathvariant="script">H n \mathfrak{m}=c\mathscr{H}^{n} some > 0 c>0 , where open ???? – possibly collapsed essential dimension ????.
منابع مشابه
The collapsed athlete.
Athletic collapse is rare, but personnel caring for athletes at sporting events must be prepared for it. Most cases are nonfatal and, with proper management, can have good outcomes. Medical personnel should expect the typical causes of athletic collapse that occur at the events they are covering, but rare causes should also be anticipated.
متن کاملCollapsed Blocks Approximations
The collapsed blocks approximations (CBAs) are a class of approximations to multivariate distributions based on full conditional distributions for blocks of variables. The CBAs are useful when the full conditional distributions are known and computationally cheap to sample from and evaluate (i.e. for Markov models). In addition knowledge about the dependence structure is needed (e.g. spatial mo...
متن کاملLocally Collapsed 3-manifolds
We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.
متن کاملCollapsed Variational Inference for HDP
A wide variety of Dirichlet-multinomial ‘topic’ models have found interesting applications in recent years. While Gibbs sampling remains an important method of inference in such models, variational techniques have certain advantages such as easy assessment of convergence, easy optimization without the need to maintain detailed balance, a bound on the marginal likelihood, and side-stepping of is...
متن کاملCollapsed Variational Inference for LDA
1 LDA We shall follow the same notation as Blei et al. (2003). In other words, we consider full LDA model with hyperparameters α and η on β and θ respectively, where θ parameterizes P (topic|document) and β parameterizes P (word|topic), wdn refers to n-th word of the d-th document. zdn refers to the topic that generates the n-th word of the d-th document. 1.1 Variational Inference Setup Cost fu...
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: Crelle's Journal
سال: 2022
ISSN: ['1435-5345', '0075-4102']
DOI: https://doi.org/10.1515/crelle-2022-0071