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.
Dimer Models and Calabi-Yau Algebras
Dimer Models and Calabi-Yau Algebras - 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 Dimer Models and Calabi-Yau Algebras write by Nathan Broomhead. This book was released on 2012-01-23. Dimer Models and Calabi-Yau Algebras available in PDF, EPUB and Kindle. In this article the author uses techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. He further shows that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a `superpotential'. Some examples are Calabi-Yau and some are not. The author considers two types of `consistency' conditions on dimer models, and shows that a `geometrically consistent' dimer model is `algebraically consistent'. He proves that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows him to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models.
The Lin-Ni's Problem for Mean Convex Domains
The Lin-Ni's Problem for Mean Convex Domains - 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 The Lin-Ni's Problem for Mean Convex Domains write by Olivier Druet. This book was released on 2012. The Lin-Ni's Problem for Mean Convex Domains available in PDF, EPUB and Kindle. The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
$n$-Harmonic Mappings between Annuli
$n$-Harmonic Mappings between Annuli - 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 $n$-Harmonic Mappings between Annuli write by Tadeusz Iwaniec. This book was released on 2012. $n$-Harmonic Mappings between Annuli available in PDF, EPUB and Kindle. Iwaniec and Onninen (both mathematics, Syracuse U., US) address concrete questions regarding energy minimal deformations of annuli in Rn. One novelty of their approach is that they allow the mappings to slip freely along the boundaries of the domains, where it is most difficult to establish the existence, uniqueness, and invertibility properties of the extremal mappings. At the core of the matter, they say, is the underlying concept of free Lagrangians. After an introduction, they cover in turn principal radial n-harmonics, and the n-harmonic energy. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
The Goodwillie Tower and the EHP Sequence
The Goodwillie Tower and the EHP Sequence - 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 The Goodwillie Tower and the EHP Sequence write by Mark Behrens. This book was released on 2012. The Goodwillie Tower and the EHP Sequence available in PDF, EPUB and Kindle. The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime $2$. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the $P$ map, and the Goodwillie differentials to the $H$ map. Furthermore, he studies an iterated Atiyah-Hirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the $2$-primary unstable stems through the Toda range (up to the $19$-stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of Dyer-Lashof-like operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod $2$ stable homology of the Goodwillie layers of any functor from spaces to spaces.
