相关论文: A nice lima\c{c}on-like spiral
The metric approach to studying 2-step nilpotent Lie algebras by making use of non-degenerate scalar products is realised. We show that any 2-step nilpotent Lie algebra is isomorphic to its standard pseudo-metric form, that is a 2-step…
We construct complete, finite volume, 4-dimensional manifolds with sectional curvature $-1<K<0$ with cusp cross sections compact solvmanifolds.
We give examples of spin $4$-manifolds with boundary $(M,\partial M)$ such that the boundary $\partial M$ has a positive scalar curvature metric which cannot be extended to a positive scalar curvature metric on $M$ with mean convex…
Every 4-connected graph with minimum degree $\delta$ and connectivity $\kappa$ either has a cycle of length at least $4\delta-2\kappa$ or has a dominating cycle.
We consider multiple radial SLE curves with various time parameterizations and possible spiraling behavior. We construct them by tilting independent radial SLEs with a suitable local martingale, generalizing the earlier construction by…
Let $X$ be a semistable curve and $L$ a line bundle whose multidegree is uniform, i.e., in the range between those of the structure sheaf and the dualizing sheaf of $X$. We establish an upper bound for $h^0(X,L)$, which generalizes the…
We describe all triangles that shares either circumcircle and pedal circle or circumcircle and negative-pedal circle. Neither of these pairs is poristic; nevertheless, the negative-pedal curve of the pedal-circle is a (very) special i-conic…
We confirm a conjecture of Hamilton: On compact manifolds the normalized Ricci flow evolves metrics with positive curvature operators to limit metrics with constant curvature.
The topological classification of gradient like Morse-Smale vector fields and diffeomorphisms on 3-manifolds was obtained.
In this paper, a lot of examples of four-dimensional manifolds with an almost hypercomplex pseudo-Hermitian structure are constructed in several explicit ways. The received 4-manifolds are characterized by their linear invariants in the…
The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn…
We consider spherical quadrangulations -- spherical embeddings of multigraphs, possibly with loops, so that every face has boundary walk of length 4 -- in which all vertices have degree 3 or 4. Interpreting each degree 4 vertex as a…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
The mirror curves enable us to study B-model topological strings on non-compact toric Calabi--Yau threefolds. One of the method to obtain the mirror curves is to calculate the partition function of the topological string with single brane.…
We study the lattices of algebraic and transcendental cycles of cubic fourfolds.
The amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real subspace in the logarithmic scale. The complement to an amoeba is a disjoint union of connected components that are open and…
On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…
Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this thesis we explore this correspondence to classify smooth lattice…
We use the Dirac operator method to prove a scalar-mean curvature comparison theorem for spin manifolds which carry iterated conical singularities. Our approach is to study the index theory of a twisted Dirac operator on such singular…
In this paper we consider the birational classification of pairs (S,L), with S a rational surfaces and L a linear system on S. We give a classification theorem for such pairs and we determine, for each irreducible plane curve B, its…