Book Review: Non-linear elliptic equations in conformal geometry
نویسندگان
چکیده
منابع مشابه
Elliptic Equations in Conformal Geometry
A conformal transformation is a diffeomorphism which preserves angles; the differential at each point is the composition of a rotation and a dilation. In its original sense, conformal geometry is the study of those geometric properties preserved under transformations of this type. This subject is deeply intertwined with complex analysis for the simple reason that any holomorphic function f(z) o...
متن کاملOn a fully non-linear elliptic PDE in conformal geometry
We give an expository survey on the subject of the Yamabe-type problem and applications. With a recent technique in hand, we also present a simplified proof of the result by Chang-Gursky-Yang on 4-manifolds.
متن کاملNon-linear Partial Differential Equations in Conformal Geometry
In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conformal invariants have been introduced. The conformally covariant powers of the La...
متن کاملDifferentiability Theorems for Non - Linear Elliptic Equations
^ C O and Z)0(x) stand for ——^ ^ " ^ T » (bx ) . . . (o* ) y and Dz stands for all the derivatives Dz for i = \, . . . , N and 0 < |a| < mt (of course if |a | = 0 , Dz = z). Equations of the form (1 ) were discussed in my paper "Partial regularity theorems for elliptic systems" which appeared in the January 1968 issue of the Journal of Mathematics and Mechanics [17] where it was assumed that th...
متن کاملBifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations
In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...
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: Bulletin of the American Mathematical Society
سال: 2007
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-07-01136-6