Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I write by Mark P. Walsh. This book was released on 2011. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I available in PDF, EPUB and Kindle. It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. The author shows that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.
Metrics of Positive Scalar Curvature and Generalised Morse Functions
Metrics of Positive Scalar Curvature and Generalised Morse Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metrics of Positive Scalar Curvature and Generalised Morse Functions write by Mark P. Walsh (Matematico). This book was released on 2010. Metrics of Positive Scalar Curvature and Generalised Morse Functions available in PDF, EPUB and Kindle.
Supported Blow-Up and Prescribed Scalar Curvature on $S^n$
Supported Blow-Up and Prescribed Scalar Curvature on $S^n$ - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Supported Blow-Up and Prescribed Scalar Curvature on $S^n$ write by Man Chun Leung. This book was released on 2011. Supported Blow-Up and Prescribed Scalar Curvature on $S^n$ available in PDF, EPUB and Kindle. The author expounds the notion of supported blow-up and applies it to study the renowned Nirenberg/Kazdan-Warner problem on $S^n$. When $n \ge 5$ and under some mild conditions, he shows that blow-up at a point with positive definite Hessian has to be a supported isolated blow-up, which, when combined with a uniform volume bound, is a removable singularity. A new asymmetric condition is introduced to exclude single simple blow-up. These enable the author to obtain a general existence theorem for $n \ge 5$ with rather natural condition.
A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations
A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations write by Greg Kuperberg. This book was released on 2012. A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations available in PDF, EPUB and Kindle. In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.
Positive Definiteness of Functions with Applications to Operator Norm Inequalities
Positive Definiteness of Functions with Applications to Operator Norm Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Positive Definiteness of Functions with Applications to Operator Norm Inequalities write by Hideki Kosaki. This book was released on 2011-06-10. Positive Definiteness of Functions with Applications to Operator Norm Inequalities available in PDF, EPUB and Kindle. Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.
