Schulze, B.-W. Seiler, J.
Published in
The Journal of Geometric Analysis

We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We p...

Prats, Martí Saksman, Eero
Published in
The Journal of Geometric Analysis

Given any uniform domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}, the Triebel–Lizorkin space Fp,qs(Ω)\documentclass[12pt]{minimal} \use...

Evert, Eric Helton, J. William Klep, Igor McCullough, Scott
Published in
The Journal of Geometric Analysis

For matrix convex sets, a unified geometric interpretation of notions of extreme points and of Arveson boundary points is given. These notions include, in increasing order of strength, the core notions of “Euclidean” extreme points, “matrix” extreme points, and “absolute” extreme points. A seemingly different notion, the “Arveson boundary”, has by ...

Takeuchi, Yuya
Published in
The Journal of Geometric Analysis

A formula of the renormalized volume of tubes over polarized Kähler–Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.

Lam, Casey Lauer, Joseph
Published in
The Journal of Geometric Analysis

In this note we prove that the level-set flow of the topologist’s sine curve is a smooth closed curve. In Lauer (Geom Funct Anal 23(6): 1934–1961, 2013) it was shown by the second author that under the level-set flow, a locally connected set in the plane evolves to be smooth, either as a curve or as a positive area region bounded by smooth curves. ...

Clerc, Jean-Louis
Published in
The Journal of Geometric Analysis

Let X=G/P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X=G/P$$\end{document} be a real projective quadric, where G=O(p,q)\documentclass[12pt]{minimal} \usepackage{ams...

Nagy, Ákos
Published in
The Journal of Geometric Analysis

Ginzburg–Landau fields are the solutions of the Ginzburg–Landau equations which depend on two positive parameters, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alp...

Sakurai, Yohei
Published in
The Journal of Geometric Analysis

We study Riemannian manifolds with boundary under a lower N-weighted Ricci curvature bound for N at most 1, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and various splittin...

Kalvin, Victor
Published in
The Journal of Geometric Analysis

Let m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {m}}$$\end{document} be any conical (or smooth) metric of finite volume on the Riemann sphere CP1\document...

Galaev, Anton S.
Published in
The Journal of Geometric Analysis

The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential. Complex pp-waves are charact...