arXiv research

Smooth manifolds from locally homogeneous spaces.

Smooth Riemannian manifolds can be embedded without boundary.

We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a string manifold is a per-Hilbert-Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.

Riemannian metrics and Laplacians defined for complex distributions on manifolds.

Smooth projections on manifolds split into simpler parts.

Smooth solutions found for modified mean curvature flow in Riemannian manifolds.

Proof shows smooth minimal hypersurfaces for perimeter-minimizing sets in low-dimensional Riemannian manifolds.

Survey on gluing constructions under lower curvature bounds.

Survey on smooth function and form density in Riemannian Sobolev spaces.

The study extends calibrated geometry to smooth maps and finds energy bounds.

Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local Lp space or if g is continuous. In this work we define a mollifier smoothing g_t of g that has the following feature: If g is a Riemannian metric of class C2, then the Levi-Civita connection and the Rieman…

Riemannian gradient descent helps escape saddle points on curved spaces.

The study proves smoothness and estimates for $p$-harmonic mappings between Riemannian manifolds.

We establish combinatorial versions of various classical systolic inequalities. For a smooth triangulation of a closed smooth manifold, the minimal number of edges in a homotopically non-trivial loop contained in the $1$-skeleton gives an integer called the combinatorial systole. The number of top-dimensional simplices…

Smooth submetries between curved spaces are smooth.

New obstruction found for smoothability of certain 4-manifolds.

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $ε:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leqε(p)$ for every …

Smooth families of biholomorphisms between strongly pseudoconvex domains are shown to be smooth.

Generic smooth boundaries for isoperimetric regions in 8D manifolds.

Smooth approximation of integral cycles mod 2 in Riemannian manifolds.

We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.

Proves stable smooth minimal hypersurface for trapped region boundary in large dimensional manifolds.

Study rough Riemannian metrics on manifolds, proving their connectedness and completeness.

Develops calculus on Wasserstein spaces for Riemannian manifolds.

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free action of a compact Lie group. We then extend a well-known result of Nomizu and Ozek…

The paper investigates exotic smooth structures on manifolds with group actions.

We prove here that given a proper isometric action $K\times M\to M$ on a complete Riemannian manifold $M$ then every continuous isometric flow on the orbit space $M/K$ is smooth, i.e., it is the projection of an $K$-equivariant smooth flow on the manifold $M$. As a direct corollary we infer the smoothness of isometric …

Let $M^n$ be a complete, non-compact and $C^\infty$-smooth Riemannian manifold with nonnegative sectional curvature. Suppose $\Cal S$ is a soul of $M^n$. Then any distance non-increasing retraction $Ψ: M^n \to \Cal S$ must give rise to a $C^\infty$-smooth Riemannian submersion.

Smooth approximations of Lipschitz maps via Ehresmann fibrations and Reeb sphere theorem for functions.

Locally homogeneous RCD spaces are shown to be smooth manifolds.

Smooth approximation of integral cycles in manifolds.

Let $M$ be a Riemannian manifold with a polar action by the Lie group $G$, with section $Σ\subset M$ and generalized Weyl group $W$. We show that restriction to $Σ$ is a surjective map from the set of smooth $G$-invariant tensors on $M$ onto the set of smooth $W$-invariant tensors on $Σ$. Moreover, we show that every s…

The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.

The paper extends geometric inequalities from Euclidean space to Riemannian manifolds.

The paper studies convergence of discrete harmonic maps to smooth ones.

New proof shows travel time differences on boundary uniquely identify Riemannian manifold.

Study on heat trace on sub-Riemannian manifolds using probabilistic methods.

We smooth the singularities of a strictly hyperbolized smooth cube manifold.

The paper proves rigidity of scalar curvature on Riemannian manifolds.

The study connects polyhedral manifolds to Riemannian ones with geometric bounds.

New subharmonicity concept proves conjecture on Riemannian manifolds.

Smooth bundles with rough data maintain Hodge kernel isomorphism.

Study solves Gel'fand's inverse problem in non-smooth spaces with Ricci curvature bounds.

The study proves a compactness theorem for manifolds with specific curvature conditions.

New heat dispersion laws established for smooth compact manifolds.

Smooth metrics satisfying Penrose inequality are necessarily smooth.

The paper explores complex Poisson structures on smooth functions in complex manifolds.

Theory of covariant Schrödinger semigroups on Riemannian manifolds developed.