Convexity estimates for mean curvature flow and singularities of mean convex surfaces

G Huisken, C Sinestrari - 1999 - projecteuclid.org
Let F0: 2~ 4-~ R+ 1 be a smooth immersion of a closed n-dimensional hypersurface of
nonnegative mean curvature in Euclidean space, n~> 2. The evolution of A~ o= Fo (J~ 4) by …

On estimates for complex Monge-Ampère equations

B Guo, D Phong, F Tong - Annals of Mathematics, 2023 - projecteuclid.org
A PDE proof is provided for the sharp L^∞ estimates for the complex Monge-Ampère
equation that had required pluripotential theory before. The proof covers both cases of fixed …

On the Dirichlet problem for Hessian equations

NS Trudinger - 1995 - projecteuclid.org
On the Dirichlet problem for Hessian equations Page 1 Acta Math., 175 (1995), 151-164 On
the Dirichlet problem for Hessian equations by NEIL S. TRUDINGER(1) The Australian …

Flow of nonconvex hypersurfaces into spheres

C Gerhardt - Journal of Differential Geometry, 1990 - projecteuclid.org
The flow of surfaces by functions of their principal curvatures has been intensively studied. It
started with the work of Brakke [1], who used the formalism of geometric measure theory; a …

Contraction of convex hypersurfaces in Euclidean space

B Andrews - Calculus of Variations and Partial Differential …, 1994 - Springer
We consider a class of fully nonlinear parabolic evolution equations for hypersurfaces in
Euclidean space. A new geometrical lemma is used to prove that any strictly convex …

[PDF][PDF] Hypersurfaces of constant curvature in space forms

H Rosenberg - Bull. Sci. Math, 1993 - Citeseer
In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where
curvature means one of the symmetric functions of curvature associated to the second …

Fully non-linear elliptic equations on compact Hermitian manifolds

G Székelyhidi - Journal of Differential Geometry, 2018 - projecteuclid.org
We derive a priori estimates for solutions of a general class of fully non-linear equations on
compact Hermitian manifolds. Our method is based on ideas that have been used for …

[KNIHA][B] Global affine differential geometry of hypersurfaces

AM Li, U Simon, G Zhao, Z Hu - 2015 - degruyter.com
This book draws a colorful and widespread picture of global affine hypersurface theory up to
the most recent state. Moreover, the recent development revealed that affine differential …

A variational theory of the Hessian equation

KS Chou, XJ Wang - … on Pure and Applied Mathematics: A …, 2001 - Wiley Online Library
By studying a negative gradient flow of certain Hessian functionals we establish the
existence of critical points of the functionals and consequently the existence of ground states …

Gauduchon metrics with prescribed volume form

G Székelyhidi, V Tosatti, B Weinkove - 2017 - projecteuclid.org
Acta Mathematica 2017.219.1.6 Page 1 Acta Math., 219 (2017), 181–211 DOI: 10.4310/ACTA.2017.v219.n1.a6
c 2017 by Institut Mittag-Leffler. All rights reserved Gauduchon metrics with prescribed volume …