It worked. My Code:

    Mesh mesh = new Mesh();
    mesh.vertices = newVertices;
    mesh.uv = newUV;
    mesh.triangles = newTriangles;
    GetComponent<MeshFilter>().mesh = mesh;
    mesh.SetIndices(new int[] { 0 }, MeshTopology.Points, 0);

The last line creates was very important to create a trinagle. For saving the Mesh:

AssetDatabase.CreateAsset(m1, "Assets/" + "oneVertexMesh" + ".asset"); // saves to "assets/" AssetDatabase.SaveAssets();

It worked. My Code:

    Mesh mesh = new Mesh();
    mesh.vertices = newVertices;
    mesh.uv = newUV;
    GetComponent<MeshFilter>().mesh = mesh;
    mesh.SetIndices(new int[] { 0 }, MeshTopology.Points, 0);

The last line creates was very important to create a trinagle. For saving the Mesh:

AssetDatabase.CreateAsset(m1, "Assets/" + "oneVertexMesh" + ".asset"); // saves to "assets/" AssetDatabase.SaveAssets();