arXiv subjects

Felix Schulze

Publications and source records attributed to Felix Schulze.

50 records · Page 3Linked to original sources

arXiv2018

Declining rotation curves at $z=2$ in $Λ$CDM galaxy formation simulations

Selecting disk galaxies from the cosmological, hydrodynamical simulation Magneticum Pathfinder we show that almost half of our poster child disk galaxies at $z=2$ show significantly declining rotation curves and low dark matter fractions, very similar to recently reported observations. These galaxies do not show any anomalous behavior, reside in standard dark matter halos and typically grow significantly in mass until $z = 0$, where they span all morphological classes, including disk galaxies matching present day rotation curves and observed dark matter fractions. Our findings demonstrate that declining rotation curves and low dark matter fractions in rotation dominated galaxies at $z=2$ appear naturally within the $Λ$CDM paradigm and reflect the complex baryonic physics, which plays a role at the peak epoch of star-formation. In addition, we find some dispersion dominated galaxies at $z=2$ which host a significant gas disk and exhibit similar shaped rotation curves as the disk galaxy population, rendering it difficult to differentiate between these two populations with currently available observation techniques.

astro-ph.GA↗

arXiv2017

On the Kinematics, Stability and Lifetime of Kinematically Distinct Cores: A Case Study

We present a case study of a early-type galaxy (ETG) hosting a kinematically distinct core (KDC) formed in a binary high resolution 1:1 spiral galaxy merger simulation. The runtime of the simulation is pushed up to 10Gyr to follow the complete evolution of various physical properties. To investigate the origin of the KDC, the stellar component residing within the KDC is dissected, revealing that the rotational signal is purely generated by stars that belong to the KDC for at least 0.5Gyr and are newly formed during the merging process. Following the orientation of the total stellar angular momentum of the KDC, we show that it performs a motion comparable to the precession of a gyroscope in a gravitational potential. We draw the conclusion that the motion of the KDC is a superposition of an intrinsic rotation and a global precession that gets gradually damped over cosmic time. Finally, the stability of the KDC over the complete runtime of the simulation is investigated by tracing the evolution of the widely used $λ_{R}$ parameter and the misalignment angle distribution. We find that the KDC is stable for about 3Gyr after the merger and subsequently disperses completely on a timescale of ~1.5Gyr.

astro-ph.GA↗

arXiv2017

A local regularity theorem for mean curvature flow with triple edges

Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-time existence of the flow starting from an initial surface cluster that has triple edges, but no higher order junctions.

math.DG↗

arXiv2012

Expanding solitons with non-negative curvature operator coming out of cones

We consider Ricci flow of complete Riemannian manifolds which have bounded non-negative curvature operator, non-zero asymptotic volume ratio and no boundary. We prove scale invariant estimates for these solutions. Using these estimates, we show that there is a limit solution, obtained by scaling down this solution at a fixed point in space. This limit solution is an expanding soliton coming out of the asymptotic cone at infinity.

math.DG↗

arXiv2012

The half-space property and entire positive minimal graphs in M x R

We show that a properly immersed minimal hypersurface in M x R_+ equals some M x {c} when M is a complete, recurrent n-dimensional Riemannian manifold with bounded curvature. If on the other hand, M has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over M.

math.DG↗

arXiv2011

Uniqueness of compact tangent flows in Mean Curvature Flow

We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That is the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings. Furthermore, given such a closed, multiplicity-one, smoothly embedded self-similarly shrinker $Σ$, we show that any solution of the rescaled flow, which is sufficiently close to $Σ$, with Gaussian density ratios greater or equal to that of $Σ$, stays for all time close to $Σ$ and converges to a possibly different self-similarly shrinking solution $Σ'$. The central point in the argument is a direct application of the Simon-Łojasiewicz inequality to Huisken's monotone Gaussian integral for Mean Curvature Flow.

math.DG↗

arXiv2010

Stability of hyperbolic space under Ricci flow

We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the scaled Ricci harmonic map heat flow of such a metric converges smoothly, uniformly and exponentially fast in all C^k-norms and in the L^2-norm to the hyperbolic metric as time approaches infinity. We also prove a related result for the Ricci flow and for the two-dimensional conformal Ricci flow.

math.DG↗

arXiv2009

Foliations of asymptotically flat manifolds by surfaces of Willmore type

The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with nonzero mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of General Relativity.

math.DG↗

arXiv2007

Evolution of convex lens-shaped networks under curve shortening flow

We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.

math.DG↗

arXiv2007

Stability of Euclidean space under Ricci flow

We study the Ricci flow for initial metrics which are C^0 small perturbations of the Euclidean metric on R^n. In the case that this metric is asymptotically Euclidean, we show that a Ricci harmonic map heat flow exists for all times, and converges uniformly to the Euclidean metric as time approaches infinity. In proving this stability result, we introduce a monotone integral quantity which measures the deviation of the evolving metric from the Euclidean metric. We also investigate the convergence of the diffeomorphisms relating Ricci harmonic map heat flow to Ricci flow.

math.DG↗

arXiv2007

Self-similarly expanding networks to curve shortening flow

We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.

math.DG↗

arXiv2006

No mass drop for mean curvature flow of mean convex hypersurfaces

A possible evolution of a compact hypersurface in R^n by mean curvature past singularities is defined via the level set flow. In the case that the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. We obtain as a consequence that no mass drop can occur along such a flow. As a further application of the techniques used above we give a new variational formulation for mean curvature flow of mean convex hypersurfaces.

math.AP↗

arXiv2006

Nonlinear evolution by mean curvature and isoperimetric inequalities

Evolving smooth, compact hypersurfaces in R^{n+1} with normal speed equal to a positive power k of the mean curvature improves a certain 'isoperimetric difference' for k >= n-1. As singularities may develop before the volume goes to zero, we develop a weak level-set formulation for such flows and show that the above monotonicity is still valid. This proves the isoperimetric inequality for n <= 7. Extending this to complete, simply connected 3-dimensional manifolds with nonpositive sectional curvature, we give a new proof for the Euclidean isoperimetric inequality on such manifolds.

math.DG↗

arXiv2005

Stability of translating solutions to mean curvature flow

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates.

math.DG↗