Last passage isometries for the directed landscape

Consider the restriction of directed landscape $${\mathcal {L}}(x, s; y, t)$$ to a set form $$\{x_1, \dots , x_k\} \times \{s_0\} {\mathbb {R}}\times \{t_0\}$$ . We show that on any such set, is given by last passage problem across k locally Brownian functions. The functions in this isometry are built from certain marginals extended landscape. As applications construction, we Airy difference profile absolutely continuous with respect local time, KPZ fixed point started two narrow wedges has Brownian-Bessel decomposition around its cusp point, and function geodesic shapes.