Singularities ofJ-holomorphic curves in almost complex 4-manifolds

This note concerns the structure of singularities of mapsf from a neighborhood of {0} in the complex plane ? to an almost complex manifold (V, J), which areJ-holomorphic in the sense thatdf oi =J odf and are singular (i.e.,df = 0) at {0}. The main result is that whenV has dimension 4, the topology of these singularities is the same as in the case whenJ is integrable. Thus, if the image Imf =C is not multiply-covered, there is a neighborhoodU of the pointx = f(0), such that the pair (U, U ∩C) is homeomorphic to the cone overS ³,K _x whereK _x is an algebraic knot in S³ that depends only on the germC atx.     

Symplectic manifolds with contact type boundaries

Summary An example of a 4-dimensional symplectic manifold with disconnected boundary of contact type is constructed. A collection of other results about symplectic manifolds with contact-type boundaries are derived using the theory ofJ-holomorphic spheres. In particular, the following theorem of Eliashberg-Floer-McDuff is proved: if a neighbourhood of the boundary of (V, ) is symplectomorphic to a neighbourhood ofS ^2n–1 in standard Euclidean space, and if vanishes on all 2-spheres inV, thenV is diffeomorphic to the ballB ²ⁿ.Oblatum 19-III-1990Partially supported by NSF grant no: DMS 8803056     

Symplectic packings and algebraic geometry

Oblatum 9-XI-1992 & 17-VI-1993     

Symplectic embeddings and continued fractions: a survey

As has been known since the time of Gromov’s Non-squeezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. After surveying some of the most important ways of measuring the size of a symplectic set, these notes discuss some recent developments concerning the question of when a 4-dimensional ellipsoid can be symplectically embedded in a ball. This problem turns out to have unexpected relations to the properties of continued fractions and of exceptional curves in blow ups of the complex projective plane. It is also related to questions of lattice packing of planar triangles.     

Laser plasma thruster

The laser plasma thruster (LPT) is a new microthruster for small satellites. We report on development and testing of a prototype LPT. Some advantages of the LPT are: thruster voltage 4 V, mass less than 1 kg, power-to-thrust ratio 10 kW/N, and I_sp up to 1000 s. Typical thrust level is 250 μN with PVC fuel. Thrust of 1 mN is expected with energetic fuel. The pre-prototype continuous-thrust experiment includes the laser mount and heat sink, lens mounts, and focusing mechanism, which are coupled to the target-material transport mechanism. The target material is applied to a transparent plastic tape, and the laser is focused on a series of tracks on the tape. The tape-drive hardware and laser-drive electronics are described. Design, construction, and calibration of the thrust stand are described. During continuous operation, the exhaust plume is deflected in the direction of the moving tape. When the laser is operated in pulsed mode, the exhaust plume is perpendicular to the tape (parallel to the optical axis). This provides some thrust-vector control. Measured thrust is 70 μN with PVC fuel, and 550 μN with energetic fuel, with a specific impulse of 350 s. Received: 7 October 2002 / Accepted: 20 January 2003 / Published online: 28 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-505-272-7203, E-mail: luke@iera.nmt.edu